The Israeli settlement freeze due to expire on Sept. 26 has posed the most immediate test to the direct talks.
Netanyahu said on Tuesday he wouldn't extend the moratorium, while Abbas said if settlement construction resumes, the peace talks will come to an end.
"What we are doing here is creating an atmosphere that is conducive to a final agreement that rests on tough decisions," Clinton said, when asked about the expiring moratorium.
"But I am absolutely convinced that these two men, for different reasons, maybe the two can actually do this," she said, hinting there might be a way out of this dilemma.
Clinton urged both sides to make concessions, stressing that she has never been in a negotiation where "one side got everything. "