Palestinian President Mahmoud Abbas and Israeli Foreign Minister Tzipi
Livni met at the UN headquarters in New York Monday to discuss the
current political situation in Israel and Palestine.  Considered
positive and constructive by both, this was the first meeting between
Palestinian and Israeli officials in four months.

The most important topic for Israel, according to Livni, was the release of captured IDF soldier Gilad Shalit, while the cessation of the military offensive in Gaza and the release of political prisoners, especially Hamas officials, was first on the Palestinian agenda.  Abbas also emphasized that Israel support the new PA unity government, which would require it to abide by previously signed agreements and further the peace process. 

Chief Palestinian negotiator Saeb Erekat said that they also discussed ways to restart the failed road map to peace in the Middle East, which was to resolve the Palestinian-Israeli conflict, end the Israeli occupation and establish a Palestinian state by 2005.

Abbas and Livni strongly suggested that a meeting take place with Israeli Prime Minister Ehud Olmert and Abbas as soon as possible. 

Sourced from Haaretz online