Syria has handed proposals for peace with Israel over to Turkish mediators and is waiting Israel's response, al-Assad said.
He said the future of negotiations rests on who replaces Ehud Olmert as prime minister in Israel and whether that leader is committed to pursuing peace with Syria.
Olmert's Kadima party will hold elections this month to choose a new party leader, who could replace him.
Al-Assad spoke on Thursday at a summit with the leaders of France, Turkey and Qatar to discuss stability and peace in the Middle East.
Israel was not able to send a team to the talks in Syria because of Olmert's resignation, which raised legal issues on how the state would be represented, according to Western diplomats.
Syria and Israel announced earlier this year that they were holding indirect talks, months after Israeli aircraft bombed a target in eastern Syria that the US claims was a nuclear reactor under construction.
The Syrian-Israeli peace talks topped the agenda of the summit in Damascus, with the gathered leaders expressing optimism that negotiations would move forward, despite the delay.
"The summit seeks to draft a declaration of principles that would form a basis for direct peace talks between Syria and Israel," al-Assad said.
He also said negotiations with Israel would be able to move forward "after a new American administration convinced of the peace process is in place".
"We want the support of all states, basically France, Qatar and Turkey in order to be assured that the next prime minister [of Israel] will follow the same direction Olmert had followed through his readiness for complete withdrawal from the occupied territories in order for peace to be achieved."
Al-Assad went on to warn that neighbouring Lebanon was still in a fragile state and said he was worried about foreign-backed "extremist forces" creating instability in the northern city of Tripoli.
"Anything positive accomplished in Lebanon will be worthless without a solution to extremism and the Salafist forces that are moving in Lebanon. There are countries that support these forces officially," he said.
Assad said he expected diplomatic ties to be established bewteen Syria and Lebanon by the end of this year.