Clinton has sought to use her political clout to bring renewed impetus to the flagging peace process, and has persuaded the two sides back to the negotiating table for the first time after a 20-month hiatus.
But the talks are overshadowed by the end of an Israeli moratorium on settlement building due to expire this weekend.
Abbas earlier Friday rejected an Israeli suggestion that a compromise may be possible, after Israel indicated it was willing to cut a deal acceptable to the United States and the Palestinians.
"Israel is prepared to reach a compromise acceptable to all parties," a senior Israeli government official said when asked about US President Barack Obama's call for the moratorium to be extended.
But he also stressed that "there cannot be zero construction" in West Bank settlements.
And Abbas Friday rejected any compromise that does not guarantee a "complete halt" to settlement activity, his adviser Nabil Abu Rudeina told AFP.
"A total freeze must be maintained on settlement activity in the Palestinian territories, including in Jerusalem. We reject any partial solution," he said.
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