The top US diplomat has on Sunday, the fourth day of his 10th visit to Israel and the West Bank, promised any agreed plan would be "fair and balanced." (Agencies)
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," Kerry said early on 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," Kerry said.
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."
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.
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," Kerry said.
Saudi Foreign Minister Saud al-Faisal agreed it had been "an excellent meeting."
The top US diplomat has on Sunday, the fourth day of his 10th visit to Israel and the West Bank, promised any agreed plan would be "fair and balanced."