The resumption of Israeli-Palestinian negotiations was cast into doubt after Palestinian leaders called on Israel to agree a general border of a future Palestinian state before direct negotiations continue.
The Palestinian stand, at the conclusion of two high-level meetings on Thursday, is at odds with Israel's insistence that there are no preconditions to talks.
Palestinians leaders want the guarantee to ensure talks end with a result.
Wasel Abu Yussef, a member of the Palestine Liberation Organisation's executive committee, said Palestinian officials decided to send top negotiator Saeb Erekat to meet the US Secretary of State, John Kerry, in Amman to "inform him that Palestinians want guarantees regarding the general border''.
That refers to Israel's de facto border that separates Israel from the occupied West Bank and East Jerusalem, territories that it captured in the 1967 war alongside the Gaza Strip.
Palestinians claim those territories for their future state, with modifications reached through agreed "land swaps" that would see major Jewish settlement blocks built in the West Bank becoming part of Israel in exchange for territories elsewhere.
Kerry held a surprise second meeting with Erakat early on Friday as he pressed to put a peace bid back on track before heading home.
After meeting first for 44 minutes, the two men were locked back in talks at 11:20am local time (0820 GMT) a State Department official said.
Obama urges talks
The Palestinian meetings followed months of mediation efforts by the US.
Hoping to push both sides into talks, US President Barack Obama on Thursday asked Israel's prime minister, Benjamin Netanyahu, to work with Kerry "to resume negotiations with Palestinians as soon as possible".
Netanyahu, whose rightist coalition government includes parties that back settlers in the West Bank and in East Jerusalem, says he wants to start peace talks immediately, but without preconditions.
The PLO's Yussef said negotiator Erekat would also ask for more clarifications from Kerry on what Israel expects.
He said Palestinians did not want to reject Kerry's efforts to restart negotiations outright. Another official in the meeting, said they felt pressure from Palestinians to not restart negotiations if they could not be seen producing substantive outcomes.
Palestinian President Mahmoud Abbas convened the two meetings with his advisers after a lengthy meeting with Kerry earlier this month.
Abbas, whose peace strategy is opposed by the Hamas, which rules the Gaza Strip, has sought Arab League support in the past to engage Israel.
Hamas' leader Ismail Haniyeh called Kerry's efforts "a waste of time".
Kerry has not spelled out his proposals. But his efforts won the notable endorsement of the Arab League, which said they "provide the ground and a suitable environment to start negotiations".
The US secretary of state has been shuttling for months in search of a formula to allow resumption of talks after a nearly five-year break.
Talks have been stalled since late 2008, with the status of Israeli settlements at the heart of the deadlock. That issue was not mentioned after the meetings finished.