"The talks with Kerry were about to collapse, and the letter came as a lifeline in the last-minute bargaining," one of the Palestinian officials said.
U.S. officials have said in the past that Kerry would reiterate standing American positions on the goals for renewed talks, including that a Palestinian state should be negotiated on the basis of Israel's borders before the 1967 Mideast war, when Israel captured the Gaza Strip, West Bank and east Jerusalem.
There was no immediate comment from the State Department, though a Western official denied the Palestinian officials' claim about the '67 borders.
"There are no terms of reference or any other agreements that the '67 lines will be the basis for negotiations," the official said. The official spoke on condition of anonymity as the official had no authorization to speak to the media.
After a round of intense shuttle diplomacy, Kerry announced on Friday that Israel and the Palestinians had agreed on a basis for returning to the peace process, which broke down five years ago. The two sides are to meet likely in the coming week to work out final details on actually resuming their negotiations on the toughest issues of the Israeli-Palestinian conflict.
Kerry would not give details on the agreement on the negotiations' framework. "The best way to give these negotiations a chance is to keep them private." he said. "We know that the challenges require some very tough choices in the days ahead. Today, however, I am hopeful."
The Palestinians long refused to return to the negotiating table unless Israel agreed to several preconditions, including that the talks be based on Israel's pre-1967 borders. Israel frequently called for talks to resume without preconditions, insisting that all core issues should be resolved through dialogue.
Speculation has been rife for weeks that the sides would find a way to sidestep Israel's reluctance to offer assurances of the 1967 lines as the framework for talks by having the guarantee provided by the United States.
Israeli Prime Minister Benjamin Netanyahu faces sharp opposition from within his majority coalition to such a move. One key ally, Economics Minister Naftali Bennett, has threatened to pull his Jewish Home Party out of the government altogether if the prime minister agrees to the border conditions.
The basis of the negotiations themselves not the core issues at the heart of the conflict has been a major impediment to resuming talks. On Thursday evening, the Palestinian leadership balked at dropping a main condition: They demanded a guarantee that negotiations on borders between a Palestinian state and Israel would be based on the cease-fire line that held from 1949 until the 1967 war.
Kerry's announcement late Friday suggested that the question had been resolved, although the top U.S. diplomat offered no details.
Netanyahu issued a statement Saturday evening welcoming Kerry's announcement and thanking him for his efforts, saying he "views the resumption of the political process at this time a vital strategic interest."
Earlier Saturday, Israel's intelligence and strategic affairs minister offered a few details on the framework. He confirmed that Israel would release some Palestinian prisoners, but said it will not meet other long-standing Palestinian demands before negotiations resume, such as a settlement freeze or defining the 1967 borders as the basis for talks.
Yuval Steinitz told Israel Radio that prisoners Israel has agreed to release include some who "have been sitting in jail for dozens of years," He did not say how many would be freed, adding only that they would be released in phases.
The fate of the prisoners is extremely sensitive in Palestinian society. After decades of fighting Israel, many families have had a member imprisoned and the release of prisoners has been a longstanding demand. The Palestinians are held on a range of charges, from rock throwing to deadly assaults like shooting attacks or bombings targeting Israeli soldiers and civilians. The Palestinians mostly view the prisoners as heroes while Israelis tend to see them as terrorists.
In a sign of the opposition Netanyahu faces even within his own government, deputy defense minister Danny Danon issued a statement condemning the prisoner release, saying "these murderers must not be released as an 'act of good will' or as a prize for returning to the negotiating table."
Steinitz said it a nine-month timetable was agreed to for the talks to prevent them from collapsing along the way. He also said the Palestinians agreed to refrain from taking action against Israel at the United Nations while the talks are taking place echoing the statement from the Palestinian officials.
Israel's chief negotiator with the Palestinians, Tzipi Livni, welcomed the revival of the peace process. She said it was difficult to restart talks after years of mistrust between the sides, but that she is "hopeful" about them.
"This is a very heavy responsibility," Livni told Israel's Channel 2 TV of the talks. "All the issues will be on the table."
Final status negotiations aim to reach a deal on the core issues of the Israeli-Palestinian conflict, including Jerusalem, borders, the fate of Palestinian refugees and security arrangements. Talks ground to a halt five years ago, and previous efforts to revive them have stalled, particularly over Palestinian demands that Israel announce a freeze in construction of Jewish settlements in the West Bank and east Jerusalem, which they claim as part of a future state along with Gaza. Israel withdrew from Gaza in 2005.
In Gaza, Hamas spokesman Sami Abu Zuhri said his group rejects Kerry's announcement, saying it does not recognize Abbas' "legitimacy to negotiate" on their behalf. The militant Hamas group rules Gaza, and has been at odds with Abbas since taking over the seaside strip in 2007.
Associated Press writer Matthew Lee in Washington contributed to this report.