Ehud Olmert, the Israeli prime minister, confirmed on Wednesday night that his country and Syria have been in contact for a year now.
Al Jazeera speaks to residents of the Golan Heights
"We are ready to make substantial concessions to Syria that will be quite painful," he told a gathering in Tel Aviv.
"The negotiations are going to take a long time.
"It will not be easy, and we have no illusions. I am convinced that the possibility of success is greater than the risk" involved."
His remarks were seen as a reference to the Golan Heights, the Israeli-annexed Syrian territory which was the main sticking point in past negotiations.
Olmert's cabinet colleague Ehud Barak said peace with Syria could be achieved only from a position of strength and self-confidence.
As the Israeli prime minister in 2000, Barak, currently the defence minister, took part in US-hosted talks with Syria that failed over the Golan issue.
For her part, Tzipi Livni, the Israeli foreign minister, set clear demands on Thursday for resumption of peace talks with Damascus.
She said that Syria must stop supporting Hamas and Hezbollah.
She also wants Damascus to cut its ties with Iran.