JERUSALEM (AFP) - US Secretary of State John Kerry said on Sunday, Dec 5, 2014, he had won Saudi support for his efforts to broker an Israeli-Palestinian peace deal, in a day of whistlestop diplomacy to key Arab allies.

The top US diplomat, on the fourth day of his 10th visit to Israel and the West Bank, promised any agreed plan would be "fair and balanced". And he likened his efforts to broker a compromise, and a framework for guiding the talks towards an April deadline, to figuring out a puzzle.

"In the end all of these core issues fit together like a mosaic, like a puzzle and you can't separate out one piece or another," Mr Kerry said on early Sunday before flying to Amman, and later to Saudi Arabia.

Each piece was interlinked, he stressed, and depended on the compromises the other side might be prepared to make as they sort through their competing demands.

"And there's always tension as to when you put your card on the table as to which piece you're willing to do, when and how," said Mr Kerry.

But he warned his efforts could ultimately fail, saying he could not tell when "the last pieces may decide to fall into place, or may fall on the floor, and leave the puzzle unfinished."

Mr Kerry briefed the key Jordanian and Saudi stakeholders about his intense shuttling between Israel's Prime Minister Benjamin Netanyahu and Palestinian President Mahmud Abbas over the past few days.

In Amman, he spent more than an hour with King Abdullah II and Foreign Minister Nasser Judeh.

A senior State Department official said Mr Kerry had wanted to "seek their counsel on the discussion with the Israelis and Palestinians about a framework for final status negotiations".

He then travelled to Saudi Arabia for almost three hours of talks with King Abdullah in his secluded desert residence.

He emerged from the talks saying they had been "very productive".

"Today, His Majesty was not just encouraging, but supported our efforts and hopes that we can be successful in the days ahead and believes that this is important for the region and that there are great benefits that will come to everybody if we're able to be successful," Mr Kerry said.

Saudi Foreign Minister Saud al-Faisal agreed it had been "an excellent meeting."

Jordan borders the occupied West Bank, and under its 1994 peace treaty with Israel is recognised as playing a historic role in the guardianship of Muslim sites in east Jerusalem.

Saudi Arabia's King Abdullah was the author of a 2002 Arab League peace initiative, which Kerry praised again on Sunday as holding out the prospect for "instantaneously" reaching peace between Israel and 22 Arab nations and 35 Muslim nations who have pledged to recognise Israel if there is a deal with the Palestinians.

Saudi Arabia has, however, been notably frustrated by America's perceived lack of action to halt the war in Syria, and the conflict was also addressed in Sunday's talks.

Prince Faisal dismissed the notion that the two countries were at odds, saying their meeting "belies any bad vibes about relations that were expressed in many of the media lately."

Mr Kerry kicked-started nine months of direct peace negotiations in July after a three-year hiatus. But Israeli and Palestinian officials have both traded accusations in recent days.

"The Palestinians are continuing their campaign of inciting hatred, as we have seen in the last few days with their refusal to recognise Israel as a state for the Jewish people," public radio quoted Netanyahu as telling his Cabinet on Sunday.

He was speaking after a Palestinian source said Washington was proposing a mixed Israeli-Palestinian military presence to ensure security in the Jordan Valley, without setting a deadline when Israeli troops would be withdrawn.

But Mr Kerry, who arrived back in Jerusalem on late Sunday, insisted: "I can guarantee all parties that President (Barack) Obama and I are committed to putting forward ideas that are fair, that are balanced, and that improve the security of all the people of this region."

A peace treaty would deal with all the divisive core issues, including the contours of a future Palestinian state, refugees, the fate of Jerusalem claimed by both as a capital, security and mutual recognition.