"Time is of the essence to revive the waning Middle East peace process", U.S. Secretary of State John Kerry said ahead of a second round of meetings Friday.
"I am convinced, with great humility, that this moment is a critical one for the region and particularly for Israel, for Palestine and for Jordan ", Kerry said before meeting with Israeli President Shimon Peres in Jerusalem and then traveling to Ramallah in the West Bank to meet with Palestinian Authority President Mahmoud Abbas and his aides.
"The next 18 to 24 months are essential to agreeing on key steps forward in the peace process and the creation of an independent Palestinian state alongside Israel", Kerry said, adding that time frame may be generous.
Palestinian officials  have said they expect Kerry to present a proposal for restarting talks by early June.
Both sides have said they want to talk.
But before Kerry arrived in Ramallah -- his fourth visit to the area in eight weeks -- a Palestinian official told The New York Times he saw no indication Israel would consider meeting  Palestinian requirements to resume the long-stalled talks.
A key requirement is that Israel's continued settlement construction in the West Bank be halted.
Israeli Justice Minister and chief negotiator on the Palestinian issue Tzipi Livni Thursday told Israel Radio Israel was definitely interested in advancing the peace process.
After meeting with Kerry, she said, "The next days and weeks are critical, and it's important everyone stays focused".
But in her Israel Radio interview, Livni acknowledged differences within Prime Minister Binyamin Netanyahu's 2-month-old coalition government, pointing out the right-wing Jewish Home Party member rejects the idea of a Palestinian state.
But she said Netanyahu was fully aligned with Kerry's effort.
Netanyahu said before meeting with Kerry "resuming peace talks was something I want. It's something you want. It's something I hope the Palestinians want as well".
The official Palestinian news agency WAFA said after Kerry and Abbas met Abbas again raised key issues including Israel's settlement construction , Israeli attacks in East Jerusalem, settler violence and Israel's detention of Palestinian prisoners.
Kerry as peace broker sought to counter those on either side who doubted the possibility of a success scenario, the Times said.
"I know this region well enough to know that there is skepticism -- in some corridors, there's cynicism, Kerry said before meeting with Netanyahu. And there are reasons for it. There have been bitter years of disappointment".
But he said," It is our hope that by being methodical, careful, patient, but detailed and tenacious, that we can lay out a path ahead that could conceivably surprise people, but certainly exhaust the possibilities of peace".
Kerry was to hold another round of meetings Friday, including a working breakfast with Netanyahu, before flying to Ethiopia for a meeting of the African Union.