Israel was grappling with an uptick in Palestinian violence on Thursday after three separate incidents, two in the West Bank and one in Jerusalem, left two Israelis dead.

The three suspected Palestinian perpetrators were also confirmed dead.

Prime Minister Benjamin Netanyahu vowed that Israel would "settle accounts with whoever did this."

"Today we suffered a harsh attack in which two soldiers were killed," he said. "Our guiding principle is that whoever attacks us and whoever tries to attack us – will pay with his life. Our enemies know this and we will find them."

The Israeli army temporarily blocked access to and from the Palestinian city of Ramallah after two Israeli soldiers were killed in a shooting in at a bus stop in the West Bank. A third soldier was severely wounded and another Israeli was also in a serious condition.

The army set up checkpoints on all roads into the city after the shooting. The army said that the attacker got out of a car and shot at soldiers and civilians before fleeing by car toward Ramallah.

The army believed there was only one assailant and was searching the Ramallah area for him, army spokesman Jonathan Conricus told reporters.

Hamas lauded the attack, while the Palestinian Authority condemned the recent violence.

Palestinian media called the Israeli move a "siege."

Later in the day, an Israeli soldier was lightly wounded in what the army called an attempted car-ramming attack in the Palestinian city of al-Bireh, north-east of Ramallah.

The driver attempted to run over Israeli soldiers on duty at the location, according to the army. "Security forces who were present at the scene fired towards the terrorist and neutralized him," the army said.

Palestinian media said the Palestinian driver was a 60-year-old man who had been trying to get home and got caught in the clashes in al-Bireh on his way. Witnesses said the man appeared to have panicked and tried to drive away when he drove towards the soldiers.

Disturbances in the West Bank had been planned on Thursday morning after Israeli security forces found and killed two Palestinians who had allegedly perpetrated two separate deadly attacks in the West Bank, one on Sunday near the Ofra settlement and another two months ago in the industrial area of Barkan.

Hamas claimed responsibility for both attacks.

On Wednesday night, an Israeli baby, born prematurely after its mother was critically injured in the Ofra attack, died at a Jerusalem hospital.

Thursday's attack resembles the Ofra attack, a drive-by shooting at a bus stop just outside the settlement.

A stabbing attack also occurred Thursday morning in the Old City of Jerusalem, in which police said the assailant had attempted to stab a Jewish man and then stabbed and wounded two border police officers, who then shot and killed the attacker.

Member of parliament Uri Ariel of the far-right Jewish Home party said that in the wake of the attacks, several MPs would meet on Thursday evening "to discuss our continuation in the government and the coalition." If they leave the coalition, it will bring down the government which has a razor-thin majority in the parliament.

Netanyahu later instructed that the homes of the terrorists be demolished within 48 hours and decided to increase security and settlement building in the West Bank.

A statement put out by the office of Palestinian Authority President Mahmoud Abbas blamed "repeated incursions into the cities, incitement against the president and the absence of a horizon for peace" for the surge in violence, which it said it rejected and condemned.

Meanwhile, Abdulatif al-Qanou’a, Hamas' spokesman in Gaza, said that the shooting "was a response to the crimes and behaviour of the Israeli occupation."

"The men and the youths of the West Bank will carry on being revolutionists in the face of the occupation and will remain in a status of a permanent confrontation with it until it is defeated," he said.

UN Secretary General Antonio Guterres said he was "deeply concerned" about the recent violence and urged Israeli and Palestinian security services to work together to restore calm and avoid an escalation.

Guterres "condemns all acts of violence and terrorism, in particular against innocent civilians," his spokesman Farhan Haq said Thursday.

Israel occupied the West Bank, which is claimed by Palestinians for their future state, in the 1967 Six-Day War.

Much of the international community considers Israeli settlements illegal and an impediment to the Israeli-Palestinian peace process.