RIYADH - Secretary of State John Kerry Sunday rejected Israeli and Palestinian claims the US was biased as he made a whistlestop tour of allies Jordan and Saudi Arabia to woo support for his peace plan.Kerry promised any agreed plan would be "fair and balanced" and likened his efforts to broker a compromise between the conflicting demands of the two sides to 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," Kerry said in Jerusalem before flying to Amman, and later Saudi Arabia.Each piece was interlinked, he stressed, and depended on the compromises the other side might be prepared to make. "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 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. That's exactly what makes this such a challenge."On the fourth day of his long trip to the region, Kerry was briefing the key Jordanian and Saudi stakeholders about his intense shuttling between Israel's Prime Minister Benjamin Netanyahu and Palestinian president Mahmud Abbas.On Sunday, he held more than an hour of talks with Jordan's King Abdullah II and Foreign Minister Nasser Judeh.A senior State Department official said Kerry had wanted to "seek their counsel on the discussion with the Israelis and Palestinians about a framework for final status negotiations."He then flew to Saudi Arabia for talks with King Abdullah at his desert residence outside Riyadh. "Thank you so much for agreeing to see me on such short notice," Kerry told the king after arriving on a short helicopter flight from Riyadh airport. "It's a special privilege to visit you out here in the desert."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 Sunday as holding out the prospect for "instantaneously" reaching peace between Israel and "22 Arab nations and 35 Muslim nations, all of whom have said they will recognise Israel if peace is achieved."Kerry kicked-started nine months of direct 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," Netanyahu told his cabinet on Sunday."This is the main issue that we're discussing with (Kerry). Among other key topics are Israel's security, which must remain in its hands," he added, in comments broadcast by public radio.He was speaking after a Palestinian source said Washington was proposing a mixed Israeli-Palestinian military presence to ensure security in the area, without setting a deadline when the Israeli troops would be withdrawn.But Kerry 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 core issues dividing the two sides, including the contours of a future Palestinian state, refugees, the fate of Jerusalem claimed by both as a capital, security and mutual recognition.A cabinet member close to Netanyahu said Sunday Israel rejects any US-proposed security concessions for the Jordan Valley, where the West Bank borders Jordan."Security must remain in our hands. Anyone who proposes a solution in the Jordan Valley by deploying an international force, Palestinian police or technological means... does not understand the Middle East," said Intelligence Minister Yuval Steinitz.The comments came after a Palestinian source said Washington was proposing a mixed Israeli-Palestinian military presence to ensure security in the area, without setting a deadline for Israeli troops to withdraw.