Kelly charecterised Mitchell's talks with Binyamin Netanyahu, the Israeli prime minister, and Mahmoud Abbas, the Palestinian president, as "good meetings" and said there would be further opportunities to try and reach a compromise at New York.
'No middle ground'
Saeb Erekat, the chief Palestinian negotiator, agreed that efforts to try to find a way forward would continue while Abbas was in the US for the General Assembly.
"We agreed to continue meetings with the Americans," he said. "Senator Mitchell will continue his efforts in New York and after New York."
But he said that the resumption of peace talks still required Israeli movement on the settlement issue.
"We reiterated that there are no middle ground solutions for settlements. A settlement freeze is a settlement freeze," he said.
Abbas has demanded a full halt to settlement expansion in the West Bank and East Jerusalem as a condition for resuming negotiations on a final peace settlement - talks that were broken off in
Barack Obama, the US president, has endorsed that call, urging both sides to meet the terms of a 2003 US-backed "road map" for peace.
But Netanyahu has ruled out stopping construction in East Jerusalem and wants settlements in the West Bank to be able to grow to accommodate the expanding families of current settlers.
About 500,000 Israelis live in the West Bank and in Arab East Jerusalem, territory captured in a 1967 war, alongside about three million Palestinians.
The Reuters news agency quoted an unnamed Israeli government official as saying that Israel was prepared to go further than the six-month freeze previously suggested by Netanyahu.
"Israel will agree to extend the freeze beyond six months - possibly nine months, but less than a year," the official was reported as saying.
The US has pushed for a year-long freeze in settlement building.
Michael Oren, Israel's ambassador to the US, insisted efforts to find a solution were continuing.
"We've been engaged for many months now in very earnest and constructive negotiations about the settlement issue and we are close to an agreement on it," he told the US-based MSNBC network.
But Mitchell's efforts were effectively brought to an end, at least temporarily, by the onset of Israeli and Palestinian public holidays - the Jewish New Year and Muslim Eid al-Fitr.
Al Jazeera's Jacky Rowland, reporting from Jerusalem, said that hopes for a symbolic meeting between the leaders at the UN now seemed to be "slim to non-existent".
"I would say that it is the end of the beginning rather than the beginning of the end"
Philip Wilcox, former US consul in Jerusalem
"Really, Friday was the last day for Senator Mitchell to make any headway in trying to close this yawning diplomatic gap," she said.
But Philip Wilcox, a former US consul in Jerusalem and current president of the Foundation for Middle East Peace think-tank, told Al Jazeera there is still hope for the future resumption of the peace process.
"I would say that it is the end of the beginning rather than the beginning of the end," he said.
"The settlement freeze was designed as a confidence building measure, as a preliminary to real negotiations on the issues that really count.
"The real issues are borders, refugees, Jerusalem, the settlements and security."
The so-called Quartet of Middle East peace negotiators - the US, Russia, the European Union and the United Nations - still plans to hold talks on the sidelines of the General Assembly.