Israeli forces shot and injured two Palestinians when a number of protesters breached the eastern border fence and entered Israeli territory, Palestinian medical sources said on Monday evening.

The Palestinian news agency Maan reported that two Palestinians were injured with live bullets east of al-Bureij refugee camp and taken to al-Aqsa Martyrs hospital in central Gaza for treatment.

Israeli forces fired tear gas and live fire and unleashed dogs on Palestinians who crossed the border, witnesses told the news agency.

Human Rights Watch (HRW) on Sunday released a statement saying that the use of live ammunition against protesters, unless in self-defence, was unlawful, reported Anadolu Agency.

The group made the assertion after one of its researchers was struck by a rubber bullet during a protest in the West Bank.

“Indiscriminate or deliberate firing on observers and demonstrators who pose no imminent threat violates the international standards to which the Israeli security forces are bound,” the watchdog’s Executive Director Kenneth Roth said.

Hanan Ashrawi, a senior Palestinian Liberation Organization official, accused Israel on Sunday of inciting violence against Palestinians, citing recent calls by Jerusalem Mayor Nir Barkat for all Jewish Israelis to carry licensed firearms.

“Israel is provoking violence in Jerusalem and creating a situation of instability as cover to exercise control over the Al-Aqsa Mosque, transform the character of Jerusalem, annex more Palestinian land and step up its illegal settlement-building activities,” Ashrawi said.

A Palestinian was shot dead by Israeli police after attempting to stab an officer on a Jerusalem bus.

Indian President Pranab Mukherjee called for a "negotiated solution" to the Israel-Palestine conflict prior to a visit to the West Bank on Monday.

"India supports a negotiated solution resulting in a sovereign, independent, viable and united state of Palestine, with East Jerusalem as its capital, living within secure and recognised borders," the president said during a ceremony at the University of Jordan, which awarded him an honorary doctorate.

"Our bilateral relations with Israel are independent of our relations with Palestine," he said.

"India has played a proactive role in garnering support for this cause in all multilateral fora. We have called upon both sides to exercise restraint and work towards a comprehensive resolution of the Palestinian issue."

Though India has historically been supportive of the Palestinian cause, the new government of right-wing Prime Minister Narendra Modi has been keen to strengthen relations with Israel, particularly due to shared concerns over militant groups.

Mukherjee is also set to visit Al-Quds university, where he will be awarded an honorary doctorate.

On Wednesday he will travel to Israel.

Footage has been released online of Israeli settlers shouting "die, son of a bitch!" at a bleeding Palestinian boy in the Pisgat Zeev settlement in East Jerusalem, after being shot by police for allegedly stabbing two Israelis, including a 13-year old.

Israeli Prime Minister Benjamin Netanyahu said that opening a "criminal investigation" against Arab MK Haneen Zoabi and condemned other Palestinian members of the Knesset during his speech opening the Knesset's winter season.

"Knesset member [Haneen] Zoabi didn't limit herself to settlers: she justifies all acts of terror. She told a Hamas publication in sorrow and worry that 'individual acts are not enough; a full intifada is needed.' That's unbelievable. A Knesset member in Israel calls for wholesale terror against Israeli citizens. Nothing is more just than opening a criminal investigation against her. Someone who calls for murder or justifies it doesn't deserve to sit in this chamber."

"We want coexistence and we invest in the Arab sector to an extent that previous governments haven't done – on a massive scale. But, to my sorrow, one of those sitting here [MK Basel Ghattas] said: 'The Henkin couple are settlers; you can't relate to them as innocent civilians.' What does that mean? That it's acceptable to murder them?

"We are a state of laws and we will bring to justice anyone – Jew or Arab – who raises a hand against us."

MKs from the Joint List party - which is mostly composed of Palestinian citizens of Israel - walked out of the Knesset when Netanyahu began speaking. MK Issawi Freij, a Palestinian from the leftist Meretz party, was ejected from the chamber after interrupting the speech.

"Our enemies have not yet learned that terror won't defeat us," Netanyahu said. "Time after time, we are the ones who defeat them. And we will also come out of this wave of terror on top. What guides us is the understanding that our struggle is just."

"We have experienced attacks both before and after the establishment of the state; before the Six Day War and after it; when the peace process was in progress and when it stopped," the prime minister said.

"Terror is not a consequence of frustration at the lack of progress in the diplomatic process. It is clear that it comes from the desire to destroy us. That is the cause today as well."

"They are using mendacious propaganda about the Temple Mount to make trouble. There are those who say brazenly that Jews have no connection to the Temple Mount. It seems that it is possible to say anything. They say that the Jews defile the mount and repeat the lie that our intention is to destroy the Al-Aqsa Mosque or change the status quo – absolute lies.

"We are committed to maintaining the status quo on the Temple Mount and we scrupulously maintain the holy places of all religions. Were it not for Israel, Muslim extremists would have destroyed the holy places, as they're doing throughout the Middle East. We are the ones defending the religious places of all religions in Jerusalem."

Israeli police opened fire on a Palestinian man on Monday morning after he allegedly attempted to stab a police officer near the Lions' Gate of the Old City of Jerusalem.

Israeli police spokesperson Micky Rosenfeld reported that the man had "pulled a knife" at police officers.

The police officer, who was wearing a protective stab vest, was unharmed by the attack. 

Palestinian news sites quote eyewitnesses as saying that the man got into a verbal confrontation with police officers, and was not carrying a weapon when he was killed.

Witnesses told al-Quds Network that the man, who has not yet been named but is thought to have been from Jerusalem, was shot 10 times.

Amateur footage purporting to be from Jerusalem Old City shows a rapid deployment of Israeli security forces in the wake of the incident.

A poll, conducted by Israeli pollsters Midgam, has suggested the public views far-right former foreign secretary Avigdor Lieberman as most suited to dealing with security and "terrorism" in Israel.

According to the poll around 21 percent of people viewed Lieberman as best on the issue, with far-right Jewish Home leader Naftali Bennet second on 17 percent and Israeli Prime Minister Benjamin Netanyahu third on 15 percent.

Opposition leader Isaac Herzog, from the centre-left, and centrist politician Yair Lapid scored far lower, on 5 percent and 4 percent, respectively.

Palestinian Foreign Minister Riad al-Malki on Monday accused Israel of seeking to spark "a third intifada" as violence again flared in Jerusalem, the West Bank and the Gaza Strip.

"(Israeli Prime Minister Benjamin) Netanyahu wants to instigate a third intifada. He wants to avoid problems that he is facing in the political and diplomatic arena, where he has failed miserably," Malki told AFP in Vienna.

Malki said Netanyahu had committed a "grave mistake" by "violating the status quo" of East Jerusalem's Al-Aqsa compound, one of Islam's holiest sites and the holiest site in Judaism.

The site has been a flashpoint in the conflict and the scene of frequent clashes between police and Palestinian youths.

"Netanyahu is widening the scope of the conflict from a political one with the Palestinians - which always has a possibility of finding a political solution - to an unlimited war with Muslims around the world," Malki warned.

Calling on Israel to act "according to international law", he said there was nevertheless still "a possibility to contain" the crisis.

The Israeli Knesset's Foreign Affairs and Defence Committee is holding an emergency meeting on Monday to discuss a proposal to call up 1,400 reservists in the Border Guard police.

If the bill is passed it will mean that the Israeli armed forces are authorised to call up reservists, who are trained but not on active duty.

There are reports that multiple people have been wounded in a stabbing attack at a bank branch in southern Israel.

Ambulances and first responders have rushed to the scene at a branch of Bank Hapaolim, Israel's largest bank, in the small town of Kiryat Gat.

The three attacks that occurred earlier today raised fears that the bank stabbing could be related to the violence spiralling in Jerusalem and the West Bank, although Kiryat Gat is geographically isolated from the region.

However, local media were quick to clarify that the stabbing was "criminal" rather than "terrorist".

A new stabbing attack reportedly took place a few moments ago in an Israeli settlement in East Jerusalem.

Israeli police report that two young Israelis, reportedly a 13-year-old boy and a 20-year-old, were injured in an attack that took place on Monday afternoon in Pisgat Ze'ev.

The 13-year-old, named by local media as Neor Ben Ruth, was reportedly riding his bicycle around the neighbourhood when he was attacked.

One of the alleged attackers has been shot dead, while a second was injured.

Palestinian news agency Maan reports that the Palestinian who was shot dead was also under 18, although there has as yet been no official comment from the Palestinian Health Ministry to confirm this.

Pisgat Ze'ev, built on land annexed by Israel after the Six Day War, is the largest residential district in East Jerusalem.

There has been another attack, reportedly by stabbing, next to the police headquarters in Jerusalem.

One Israeli police officer was injured in the attack, which took place just a few hours after a previous, similar stabbing.

Palestinian news agency Maan reports that a 16-year-old Palestinian girl was shot and seriously injured after launching the attack, while a Palestinian man was also injured.

Amateur video and photographs purportedly from the scene show a young woman lying on the ground in a pool of blood as a team of medics rushes to the scene.

Israeli police have said the attacker was "neutralised," without specifying whether she was arrested or killed.

The attack took place in the Sheikh Jerrah district of East Jerusalem.

Earlier in the day an 18-year-old Palestinian man was shot dead near Lions' Gate in Jerusalem's Old City after allegedly attempting to stab members of the security services.

More to follow...

Israel has cancelled a scheduled trip to Ramallah and Jerusalem by the Middle East Quartet, a diplomatic mission made up of delegates from the US, Russia, the EU and the UN.

The diplomats had planned to visit the region this week to discuss calming tensions and measures to build trust between the Israelis and Palestinians.

However, Israeli objections to the planned visit meant that the plan was shelved on Monday, according to Western and Israeli diplomats who spoke to Barak Ravid, a senior political correspondent with left-leaning Israeli daily Haaretz.