Two Palestinian perpetrators attacked worshippers in the midst of morning prayers, killing and maiming their victims with meat cleavers and a gun early on Tuesday.

Cousins Ghassan and Uday Abu Jamal, from East Jerusalem, were killed by Israeli police officers who descended on the Bnei Torah synagogue in the ultra-Orthodox Jewish neighbourhood of Har Nof in West Jerusalem soon after word of the attack broke. One of the police officers died on Tuesday night of wounds he received while responding to the attack, the New York Times reported.

Three of the victims were dual Israeli-US nationals – Moshe Twersky, 59, Aryeh Kopinsky, 43, and Kalman Ze'ev Levine, 55, while the fourth was a dual Israeli-British citizen, Avraham Shmuel Goldberg, 68.

Thousands attended the funerals of the four men in Jerusalem on Tuesday afternoon.

By then Israeli security forces had set up roadblocks and checkpoints at the entrance to the attackers' neighbourhood of Jabal Mukabar and arrested at least 12 members of the Abu Jamal family.

Soon after, Prime Minister Benjamin Netanyahu ordered the demolition of the family's homes as punishment for the rabbis' deaths and directed "that enforcement against those who incite toward terrorist attacks be significantly increased".

Describing the attack as "a bloodbath", Mr Netanyahu said: "What is most shocking is not just this massacre, but the cries of joy in Gaza and Bethlehem."

He blamed the attack on "incitement" by the Islamist group Hamas, which has ruled Gaza since 2007, and the West Bank-based Palestinian President Mahmoud Abbas.

US President Barack Obama denounced the attack, describing it as a "tragedy for both nations, Israel and the US" and urging both sides to "work together to lower tensions and to reject violence".

Mr Abbas also condemned the attack, saying in a statement: "We condemn the killings of worshippers at the synagogue in Jerusalem and condemn acts of violence no matter their source."

He called for an end to the recent Israeli "provocations" surrounding the sacred site in the Old City of Jerusalem that is home to the al-Aqsa Mosque, holy to Muslims and the Temple Mount, holy to Jews.

As part of a long-standing agreement, only Muslims have the right to pray at the site, although people of other faiths may visit.

Israeli settlers, including senior members of the Israeli Parliament have renewed their attempts to push aside the status quo agreement, further escalating tensions.

By last week, tensions had escalated to such a point that Mr Netanyahu travelled to Amman to meet Jordan's King Abdullah and US Secretary of State John Kerry to call for calm.

"To my regret, the answer that we received from the Palestinian Authority was to declare a day of rage in Jerusalem," the Prime Minister said.

He spoke of Israel fighting a "lengthy war against terrorism" and denied accusations that Israel was attempting to challenge the status quo agreement at al-Aqsa Mosque.

"They are saying that the Jews are contaminating the Temple Mount. They are saying that we are planning to destroy the Holy Places, that we intend to change the order of prayer there – this is all lies."

Earlier this month, a Palestinian shot and seriously wounded the US-born hardline activist and rabbi Yehuda Glick, who has been campaigning for greater rights for Jews to pray in the compound.

The alleged attacker, Muataz Hijazi, was shot dead by police in a raid on his home early the next day.

The militant group Islamic Jihad published a memorial soon after, saying Hijazi was a member.

The synagogue murders are the deadliest attack on Jerusalem since 2008 and come after months of increasing violence in which both Israelis and Palestinians have died and calls for calm from either side have been few and far between.

The death of Palestinian bus driver Youssef al-Ramouni, 32 – found hanged in his vehicle on Monday – is believed to be one of the triggers for the synagogue attack. Palestinians allege he was killed by Israelis and Israeli police, citing autopsy results, disputed by the driver's family, that labelled his death a suicide.

"This is a very dangerous and explosive situation and the person responsible for this is Mr Netanyahu and his government," Palestinian MP Mustafa Barghouti told Fairfax Media.

"They have failed to understand the necessity of defusing the tension and instead have chosen to allow Israeli settlers to conduct their attacks inside al-Aqsa and inside Palestinian mosques."

This year alone, Israeli security forces had killed 2260 Palestinians in Gaza and the West Bank, including 600 children, Mr Barghouti said.

Most of those deaths occurred in the 50-day war in Gaza in which the UN says 2192 Palestinians were killed, 1523 of them believed to have been civilians. Sixty-six Israeli soldiers and six civilians also died in that conflict.

Those worst affected by the ongoing, decades-long Israeli military occupation – young Palestinian graduates who are facing unemployment rates of 90 cent in Gaza and 30 per cent in the West Bank – are the ones driving the protests in East Jerusalem and the West Bank, Mr Barghouti said.

"They do not see any hope or any possibility of change and they are very angry with everyone … this is a new generation, they are the ones who are laying the groundwork for a third intifada," Mr Barghouti said.

In direct contradiction with Mr Netanyahu, the head of Israel's secret service says the main factors behind the unrest were the murder of Palestinian teenager Mohamed Abu Khdeir, killed by Jewish vigilantes in retribution for the kidnapping and murder of three Israeli teens in June - and attempts by Israeli parliamentarians to change the status-quo at al-Aqsa Mosque and the Temple Mount.

"Abbas is not interested in terror and is not inciting to terror. He's not even doing so behind closed doors," Shin Bet head Yoram Cohen told the Knesset's Foreign Affairs and Defence Committee, the news site Ynet reported.

Abu Ali, the father of 21-year-old Uday, one of the men accused of killing the rabbis, described the situation as "a religious war".

His words were reflected by those of Israel's Justice Minister, Tzipi Livni, who has recently warned in local media of an attempt by politicians to turn the Israeli-Palestinian struggle into a religious conflict. On Tuesday, she told Army Radio "a religious war cannot be solved".

Although Mr Abbas condemned the attacks, a senior Hamas spokesman Musihr al-Masri wrote on his personal Facebook page: "The new operation is heroic and a natural reaction to Zionist criminality against our people and our holy places. We have the full right to revenge for the blood of our martyrs in all possible means."

The United Nations Special Co-ordinator for the Middle East Peace Process, Robert Serry, strongly condemned the attack, calling on all sides to do everything possible to avoid further escalation.

Meanwhile, the UN Office of the High Commissioner for Human Rights raised its alarm at the recent series of violent incidents in Israel and Palestine, in which near daily clashes between Palestinians and Israeli security forces are met with the use of live ammunition.

"We urge Israeli authorities to refrain from taking measures, such as punitive demolitions, which violate international law and may further inflame the situation," spokesman Rupert Coleville said, describing the death of the Palestinian bus driver as occurring in "unclear circumstances".

Over the past month, five Israelis and a visitor from Ecuador were killed after they were deliberately run over or stabbed by Palestinian attackers. At least 12 Palestinians have been also killed, including those accused of carrying out the attacks.

Many Jerusalem residents trace the latest outbreak of violence to July, when a Palestinian teenager was burned to death by Jewish attackers in an alleged revenge attack for the abduction and killing of three Jewish teens by Palestinian militants in the West Bank.

Most commentators say the outbreaks of violence are not yet co-ordinated and therefore do not necessarily signify the start of a third Palestinian intifada or uprising.

But they warn that, without a significant de-escalation in tensions – unlikely after Tuesday's deadly synagogue attack – there will undoubtedly be more violence.