US Secretary of State Antony Blinken urged "calm" and "deescalation" after violence has flared between Israel and the Palestinians, as he kicked off a Middle East tour in Cairo on Monday.

Washington's top diplomat, after meeting President Abdel Fattah al-Sisi and the country's foreign minister, left Egypt headed for Israel and the Palestinian territories.

Israel is reeling from an attack that killed seven civilians outside a synagogue in annexed east Jerusalem on Friday, a day after the deadliest army raid in years in the occupied West Bank claimed 10 lives.

"We've seen horrific terrorist attacks in the last couple of days that we condemn and deplore," Blinken told Saudi TV channel Al Arabiya.

In a press conference in Cairo on Monday, Blinken urged "all parties to calm things down and deescalate tensions" while also stressing the "importance of working for a two-state solution".

In the latest bloodshed, Israeli forces shot dead a Palestinian man in the West Bank city of Hebron, said the Palestinian health ministry -- the 35th Palestinian killed this month, according to an AFP tally based on official sources from both sides. 

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.

Blinken was later due to meet Israeli Prime Minister Benjamin Netanyahu, a veteran leader who returned to power late last year at the helm of a right-wing government, and Palestinian leader Mahmud Abbas. 

- 'Dangerous developments' -
Blinken had long planned the visit, but the trip takes on a new urgency after some of the worst violence in years.

A Palestinian gunman on Friday killed seven people outside a synagogue in a settler neighbourhood of east Jerusalem, and another attack followed on Saturday.

On Thursday, an Israeli army raid on the Jenin refugee camp in the occupied West Bank had killed 10 people, in the deadliest such operation in years.
Israel said it was targeting Islamic Jihad militants and later hit sites in the Hamas-ruled Gaza Strip in response to rocket fire.

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

The 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. 

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

- 'Death spiral' -
The latest bloodshed has heightened international concern, and Pope Francis on Sunday deplored 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.

Blinken on Monday met Sisi and then Egyptian Foreign Minister Sameh Shoukry.

Blinken commended Sisi for "Egypt's important role in promoting stability in the region" and "discussed ongoing efforts to de-escalate tensions between Israelis and Palestinians," said State Department Spokesperson Ned Price.

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

Sisi's spokesman Bassam Radi said that the "recent developments affirm the importance of working immediately within political and security frameworks to calm the situation and curtail any unilateral decision-making from either party".

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

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

The State Department said Blinken would call for the preservation of the status quo at the flashpoint Al-Aqsa mosque compound, which is holy both to Jews and Muslims. 
Itamar Ben-Gvir, a far-right ideologue who holds a security post in Netanyahu's government, in early January defiantly visited the site, which Jews call the Temple Mount.