US Secretary of State John Kerry on Thursday voiced cautious hope there may be a way to defuse Israeli-Palestinian violence that has killed nearly 60 people this month.

Speaking to reporters after about four hours of talks with Israeli Prime Minister Benjamin Netanyahu, Kerry said he thought there were steps that could reduce the violence and said they needed to be discussed with Jordanian and Palestinian officials.

"I would characterise that conversation as one that gave me a cautious measure of optimism that there may be...a way to defuse the situation and begin to find a way forward," Kerry told reporters after he met Netanyahu at a Berlin hotel.

"If parties want to try, and I believe they do, want to move to a de-escalation, there are a set of choices that are available," he told a joint news conference with German Foreign Minister Frank-Walter Steinmeier.

At a United Nations Security Council meeting on Thursday, Israeli Ambassador Danny Danon said peace could only be achieved through direct talks between the parties. He called on the international community to urge Palestinian President Mahmoud Abbas to accept an invitation from Netanyahu to meet.

Palestinian Foreign Minister Riad al-Malki said he would never dismiss the possibility of a meeting if it could help de-escalate the violence. But he added that Netanyahu would first have to "end his own incitement" and withdraw Israeli troops from the occupied Palestinian territories.

Nine Israelis have been killed in Palestinian stabbings, shootings and vehicle attacks since the start of October. Forty-nine Palestinians, including 25 assailants, among them children, have been killed in attacks and during anti-Israeli protests.

Among the causes of the turmoil is Palestinians' anger at what they see as Jewish encroachment on the al-Aqsa mosque compound in Jerusalem's Old City, Islam's holiest site outside Saudi Arabia, which is also revered by Jews as the location of two ancient temples.

The area, also home to the Dome of the Rock, is known to Muslims as the Noble Sanctuary and to Jews as the Temple Mount.

State Department spokesman John Kirby said a number of constructive proposals were suggested at Kerry's meeting with Netanyahu, including steps Israel could take to reaffirm its commitment to maintaining the status quo at Temple Mount.

"Both agreed on the need to stop incitement, reduce tension and restore calm," he added, describing the meeting as "lengthy and constructive".

Kerry made no reference to Netanyahu's suggestion this week that Haj Amin al-Husseini, the Mufti of Jerusalem during the 1940s, persuaded Adolf Hitler to exterminate the Jews.

But the White House urged against the use of inflammatory rhetoric on Thursday.

Netanyahu's comments have attracted wide criticism from Israeli opposition politicians and Holocaust experts, who accused the prime minister of distorting the historical record.

It is not clear why Netanyahu launched into the issue of the late mufti's role, with Israeli-Palestinian tensions at a new peak, notably over the Jerusalem holy site overseen by the current mufti.

Mideast Quartet meets

The European Union's senior diplomat, Federica Mogherini, also met Netanyahu and said she told him of "the need to explore together ways to stop violence, to calm down the situation".

"We discussed concrete ways to de-escalate the situation on the ground and to guarantee the status quo in the holy sites," she told reporters in Berlin.

Mogherini, the EU's foreign policy chief, said the "Quartet" of Middle East peace mediators would meet in Vienna on Friday to urge Israeli and Palestinian leaders to tone down their rhetoric and calm down the situation on the ground.

Whatever immediate steps might be taken, diplomats hold out little hope for any resumption of broader Israeli-Palestinian peace talks, which collapsed in 2014.

Netanyahu blamed the Palestinians for the recent surge in killings, singling out Abbas.

"There is no question that wave of attacks is driven directly by incitement. Incitement from Hamas, incitement from the Islamist movement in Israel, and incitement, I am sorry to say, from President Abbas," he said.

A senior US State Department official told reporters that Kerry hopes to persuade both sides to "tamp down" their rhetoric during a four-day trip to Europe and the Middle East in which he also plans to meet Abbas and Jordan's King Abdullah.