US Secretary of State Antony Blinken has called for "urgent steps" to calm spiralling violence in the Israeli-Palestinian conflict, after high-level talks in Jerusalem.

Washington's top diplomat travelled to Jerusalem on the second leg of his Middle East tour, after meeting Egypt's President Abdel Fattah al-Sisi and foreign minister in Cairo.

Israel is reeling from an attack on Friday that killed seven civilians outside a synagogue in annexed east Jerusalem, a day after the deadliest army raid in years in the occupied West Bank claimed ten Palestinian lives.

Following talks with Israeli Prime Minister Benjamin Netanyahu, Mr Blinken urged "all sides now to take urgent steps to restore calm, to deescalate".

"We want to make sure that there's an environment in which we can, I hope, at some point, create the conditions where we can start to restore a sense of security for Israelis and Palestinians alike," he said.

In the latest bloodshed, Israeli troops today killed a Palestinian driver in the West Bank, officials on both sides said, with the army saying the car had hit a soldier's leg before speeding off.

Since the start of the year, the Israeli-Palestinian conflict has claimed the lives of 35 Palestinian adults and children - including attackers, militants and civilians.

Over the same period six Israeli civilians, including a child, and one Ukrainian civilian have been killed. All were shot dead in the attack on Friday outside the synagogue in an east Jerusalem settlement.

The United States has historically taken a lead on Middle East diplomacy, and Egypt, which has relations with Israel, has long served as a mediator in the Israel-Palestinian conflict.

Following what Mr Blinken described as "very candid" discussion with Mr Netanyahu, the top US diplomat met Israeli Foreign Minister Eli Cohen.

Antony Blinken (L) and Israeli Foreign Minister Eli Cohen

Mr Blinken's envoy will also travel to Ramallah in the West Bank for talks with Palestinian leader Mahmud Abbas.

Mr Abbas met with CIA chief William Burns in Ramallah late yesterday to discuss the "dangerous developments", said the official Palestinian news agency Wafa. The US embassy declined to comment.

Mr Blinken's long-planned visit has taken on a new urgency amid the spiralling violence.

The fatal east Jerusalem shooting was preceded by the Israeli forces' deadliest operation in the West Bank in years.

Ten people were killed on Thursday in the densely populated Jenin refugee camp, in a raid Israel said targeted Islamic Jihad operatives.

The military later hit sites in the Hamas-ruled Gaza Strip in response to rocket fire from the Palestinian enclave.

Mr Netanyahu's cabinet has vowed a tough response and moved to punish "the families of terrorists that support terrorism" with home demolitions and other measures.

His government is also planning to rescind the rights to social security benefits of attackers' relatives, and steps to make it easier for Israeli citizens to obtain permits to carry firearms.

Israeli security forces stand guard in Jerusalem's predominantly Arab neighbourhood of Silwan

The latest bloodshed has heightened international concern, with Pope Francis yesterday deploring the "death spiral".

French President Emmanuel Macron urged all parties to avoid feeding a "spiral of violence" and Russia's Foreign Minister Sergei Lavrov called for "maximum responsibility" on all sides.

Mr Blinken today met Sisi and Egyptian Foreign Minister Sameh Shoukry.

He commended Sisi for "Egypt's important role in promoting stability in the region" and "discussed ongoing efforts to deescalate tensions between Israelis and Palestinians," said the State Department.

The diplomats and intelligence services of Egypt - a major recipient of US military aid - are regularly called upon to intercede between Israelis and Palestinians.

Mr Blinken's Israel visit is part of the Biden administration's efforts to engage quickly with Mr Netanyahu, who had tense relations with the previous Democratic president Barack Obama.

While there, Mr Blinken reiterated US support for a Palestinian state, a prospect few expect to advance under the new Israeli government.

Mr Netanyahu, a veteran leader, returned to power late last year at the helm of the most right-wing government in Israeli history.

In Jerusalem, Mr Blinken said he discussed with Mr Netanyahu the preservation of the status quo at the flashpoint Al-Aqsa mosque compound in east Jerusalem.

Israel's extreme-right national security minister, Itamar Ben-Gvir, sparked global condemnation this month when he visited the site which is administered by Jordan.

The compound is the holiest site to Jews, who refer to it as Temple Mount, and the third most sacred place in Islam.