Washington has made no visible progress toward its goal of reaching an outline peace deal by the end of this year and both sides appear unlikely to make any significant steps toward peace ahead of the U.S. election in November.
Clinton met Abbas after attending an international meeting on Syria, where forces loyal to President Bashar al-Assad have sought for more than a year to crush a rebellion against his family`s four-decade rule.
The Syrian conflict is the bloodiest of the Arab Spring uprisings that have toppled authoritarian rulers in Tunisia, Egypt, Libya and Yemen.
Peace talks between Israel and the Palestinians broke down in 2010 in a dispute over Jewish settlement building in the West Bank.
"In a time of upheaval across the region, we cannot lose sight of the critical importance of resolving this issue," Clinton told reporters.
Clinton is due to travel to Israel later this month. (*)