US Secretary of State John Kerry said the Israelis and Palestinians were making some progress in peace talks, though there was still a chance no accord would be reached.
Speaking before he flew to Jordan and Saudi Arabia to brief their rulers about his 10th visit to the region to see Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas, Mr Kerry said both sides had a sharper idea of the compromises needed to secure an agreement.
"This has been a productive couple of days," Mr Kerry told reporters. "We have had very positive - but I have to say very serious, very intensive conversations."
Mr Kerry said all of the major issues in the conflict -borders, security, the fate of Palestinian refugees and the status of Jerusalem were under discussion.
"The path is becoming clearer. The puzzle is becoming more defined. And it is becoming much more apparent to everybody what the remaining tough choices are," he said.
He added, he would not be flying to meet the kings of Jordan and Saudi Arabia if he did not believe both sides were grappling with the issues.
"But I cannot tell you when, particularly, the last pieces may decide to fall into place or may fall on the floor and leave the puzzle unfinished," added Mr Kerry, due to return to Jerusalem later today.
Mr Kerry appeared boosted by his meeting with Saudi King Abdullah at his winter residence near Riyadh.
"Today, His Majesty was not just encouraging but supported our efforts in (the) hopes that we can be successful in the days ahead," Mr Kerry told reporters after meeting.
Mr Kerry has been trying to establish what US officials call a "framework" for guidelines for an eventual peace accord.
He has previously asked Israel to reconsider a 2002 Arab peace plan, which it has rejected in the past.
The initiative,originally proposed by King Abdullah, offers Israel full recognition in return for giving up land it captured in 1967 and a "just" solution for Palestinian refugees.
Mr Kerry earlier spent an hour with Jordan's King Abdullah in Amman discussing the peace talks, Syria's civil war and violencein Iraq.
Elsewhere, US Secretary of State John Kerry has voiced confidence that the Iraqi government and tribes would be successful in their fight against al-Qaeda, and said Washington was not considering sending troops back to Iraq.
Sectarian and ethnic tensions have risen in Iraq since the US withdrawal in December 2011.
The tensions have been inflamed by the conflict in neighbouring Syria, where mainly Sunni rebels are trying to oust President Bashar al-Assad, who is backed by Shia Iran.
The Iraqi army has joined forces with local tribesmen to battle al- Qaeda, which has teamed up with groups of Syrian rebels to try to create across the Iraqi-Syrian border a state based on strict medieval Sunni Islamic practice.
"This is a fight that belongs to the Iraqis ... We are not contemplating returning." Mr Kerry told reporters during a visit to Israel.
"We will help them in their fight, but this fight, in the end, they will have to win and I am confident they can."
The Iraqi military's cooperation with the tribesmen against al Qaeda echoed a decision by local tribes in 2006 to join forces with US troops after the 2003 US invasion.
Baghdad bomb attacks
Iraqi government forces battling an al-Qaeda offensive launched an air strike on Ramadi city killing 25.
Two car bombs and roadside bombs have exploded in commercial areas of Baghdad killing at least 14 people, police and medical sources said.
The deadliest attack took place in northern Baghdad's mainly Shia district of Shaab, where two car bombs went off killing at least nine people and wounding 25.