The meeting takes place amid increasing fears that Mr Abbas will pull out of the talks, which resumed barely a month ago, because Israel refuses to extend a 10-month partial settlement freeze that expired on Monday.
Tomorrow Mr Abbas will consult officials from his Fatah party and the Palestine Liberation Organisation's decision-making body. The next stage will be a meeting in Cairo next week of Arab League foreign ministers. The gathering was planned for Monday, but was postponed for two days to give the US more time to rescue the peace process.
Mr Abbas is expected to have the final say on the Palestinians' next step, as Fatah and the PLO have backed his decisions in the past. The Arab League is also expected to support his stance. But Mr Abbas appears to be in a bind, because he has built his international standing on his quest for peace and walking out of the talks may harm his relationship with the US and other western countries. Sticking with the negotiations without a moratorium on settlements, however, could cost him credibility among Palestinians already sceptical of his ability to clinch a deal.
The possible exit of the Palestinians from the talks comes amid frantic efforts by the administration of Barack Obama, the US president, and the European Union to salvage the peace process. Catherine Ashton, the European Union's top diplomat, rushed to the region for a last-minute visit yesterday, saying it was "a matter of priority". Ms Ashton met Mr Abbas and the Israeli prime minister, Benjamin Netanyahu.
Mr Mitchell also met Mr Abbas for two hours yesterday at the Palestinian leader's headquarters in Ramallah. After the meeting, Mr Mitchell said the US was "determined to continue, and we are continuing, our efforts to find common ground between the parties to enable the direct negotiations to continue". Mr Mitchell did not mention the settlement dispute, although Palestinian officials suggested no progress had been made. "Apparently the Israelis are determined to swallow and steal the land and consider that much more important than peace," Nabil Shaath, an adviser to Mr Abbas, said.
"Unless the settlement activities stop completely, there is no use in continuing these negotiations." Both the US and the EU have urged Israel to extend by a few months the partial moratorium on new building projects in Jewish settlements in the occupied West Bank, which Palestinians want as part of their future state. But Mr Netanyahu has so far rejected their appeal, saying it could fracture his pro-settler governing coalition.
White House officials told Jewish politicians in Washington on Wednesday that the US was pressing Mr Netanyahu to extend the moratorium for another 60 days, according to a report in Foreign Policy magazine's blog The Cable. Such an extension would allow talks to proceed past the US midterm elections on November 2. The meeting was seen as a stepped-up White House effort to reach out to Jewish political and religious leaders in the US. Overall, Jewish members account for 8.4 per cent of both houses of Congress.
Mr Netanyahu has repeatedly urged the Palestinians to remain at the peace talks, which some Israeli commentators this week speculated may lead to a political shift within his predominantly right-wing coalition. The speculation was spurred by controversial comments by Avigdor Lieberman, the ultra-nationalist Israeli foreign minister, which pointed to sharp differences within the Israeli government over the negotiations.
Mr Lieberman used his address at the annual UN General Assembly to say that peace with the Palestinians needed an intermediate - rather than a final - agreement "lasting decades" and that the issue of Iran's nuclear ambitions should be tackled first. The remarks contradict the official position of Mr Netanyahu and the Obama administration, which is that the current direct talks be used to resolve the core issues of the conflict within a year.
While Mr Lieberman's stances are familiar to Israelis, this was one of the few times they were publicly unveiled to a high-profile international audience. The statements by Mr Lieberman, which prompted a walk-out by Palestinian delegates, spurred Israeli politicians and media commentators to call for the foreign minister's dismissal. Mr Netanyahu immediately distanced himself from the statements of Mr Lieberman, in a move suggesting tensions within the ruling coalition. The episode was coupled with speculation in recent days that Kadima, the centrist opposition party that ruled the previous government and wants to return to power, would consider joining the coalition should peace talks continue.
Such a move would allow Mr Netanyahu to drop Mr Lieberman's Yisrael Beiteinu party, currently the second-biggest in the government.