Clinton was to make a personal plea for the two sides to resume peace talks even as U.S. officials acknowledged they saw little prospect for an immediate breakthrough.
Over the course of the summer, President Barack Obama had hoped for a fast track to renewed peace negotiations, but Clinton reported to him on Oct. 22 that neither side had taken sufficient steps toward resuming the dialogue.
Clinton arrived in Abu Dhabi in the early hours Saturday after completing a three-day visit to Pakistan.
Obama held a three-way meeting with Netanyahu and Abbas in New York in September, hoping it would prod them to relaunch talks that broke off more than a year ago. But in her report to the president in October, Clinton indicated that while the Palestinians had strengthened security efforts and reforms of Palestinian institutions, more needed to be done to prevent terror and to stop those who carry out or encourage attacks on Israel.
On the Israeli side, Clinton has indicated that they have eased Palestinians' freedom of movement and expressed a willingness to curtail the building of Jewish settlements in the Palestinian areas. The Obama administration, however, is demanding an end to all new settlement construction, something which the Israelis have refused.
Clinton intends to consult with a range of Arab foreign ministers on the Israel-Palestinian stalemate when she attends an international conference in Morocco on Monday and Tuesday.
After her meeting with Abbas in Abu Dhabi, Clinton was headed for Jerusalem for talks that were expected to include not only Netanyahu but also his foreign minister, Avigdor Lieberman.
Lieberman suggested recently the Israelis and Palestinians come up with a long-term interim arrangement that would ensure stability, while at the same time putting off a final deal.
He has recommended leaving the toughest issues - such as the status of disputed Jerusalem and a solution for Palestinian refugees who lost homes in the conflict
- "to a much later stage."
Clinton also was expected to meet with Israeli Defense Minister Ehud Barack.
In an interview with the British Broadcasting Corp. before leaving Islamabad on Friday, Clinton downplayed the prospects for a quick breakthrough, while stating that former Sen. George Mitchell, the administration's special envoy on Mideast peace, was still pushing.