Israeli and Palestinian negotiators were to meet again on Monday in a fresh effort to salvage the teetering, US-brokered peace process, US and Palestinian officials said.
"Israeli and Palestinian negotiators met last night to discuss ways to overcome the crisis in the talks," a US official said.
"The meeting was serious and constructive, and both sides requested that the United States convene another meeting today (Monday) to continue the effort."
A Palestinian official confirmed to AFP that a meeting was scheduled for later Monday, but neither side gave a time or location.
Accompanied by US envoy Martin Indyk, the two sides met on Sunday evening, but Palestinian sources told AFP that the session ended without any breakthrough and an Israeli official was quoted by local media as saying the process was on the edge of collapse.
Israel's parliament was also meeting in special session on Monday during its spring recess, for a debate on the peace negotiations called by opposition MPs critical of the government's handling of the talks.
Prime Minister Benjamin Netanyahu on Sunday threatened to retaliate if the Palestinians proceed with applications to sign up to 15 international treaties.
"These will only make a peace agreement more distant," he said of the applications the Palestinians made on Tuesday.
"Any unilateral moves they take will be answered by unilateral moves at our end."
US Secretary of State John Kerry, the driving force behind the peace push, warned on Friday that there were "limits" to the time and energy Washington could devote to the talks process, as his appeals to both sides to step back from the brink fell on deaf ears.
Palestinian president Mahmud Abbas rejected Kerry's plea to withdraw the treaty applications, and Netanyahu ignored US appeals to refrain from tit-for-tat moves, asking for a range of retaliatory options.
But commentator Tal Harris wrote in the Jerusalem Post on Monday that the peace process was still alive.
"Although it might smell funny, it isn't dead yet," said Harris, of the Israeli-Palestinian dialogue movement One Voice, saying there should be teams of experts set up to work on issues such as disputes on water and energy, rather than focusing only on deadlocked political talks.
"Kerry must reveal some of the progress that was made so far, and Netanyahu and Abbas need to engage in the process more directly," he added.