Olmert told the Arab TV network Al Arabiya that he wants to resume peace talks that stalled between the two nations seven years ago, the Voice of America reported Tuesday.
However, Olmert said talks would be contingent on Syria ending support for Hezbollah, Hamas and other Islamic militant groups and scaling back ties with Iran.
"We will of course be happy to negotiate with the Syrians. We would like to make peace with Syria," said Israeli Cabinet Minister Haim Herzog. "We have a major problem with Bashar al-Assad. In order to move forward, I think Bashar al-Assad needs to show some measures of seriousness about his change in attitude."
The negotiations would focus on the Golan Heights, an area captured by Israel during the Six Day War in 1967. Syria has made a complete Israeli withdrawal from the area a condition of peace.