Israeli Prime Minister Ariel Sharon has said he will only resume talks with Syria if it "stops backing terrorism".
Sharon doesn't want to rush back into dialogue with Syria
Mr Sharon also told his cabinet on Sunday there was no need to re-start talks with Syria until reports that it wanted a dialogue were clarified.
A European Union envoy, Marc Otte, has said that Syria has indicated it is willing to resume talks.
Israeli Defence Minister Shaul Mofaz said that Syria's apparent new position was the result of US pressure.
Mr Sharon said he believed Syria was still helping agents of the Lebanese group, Hezbollah, which is accused of involvement in attacks on Israel.
He said when that support stopped, Israel would be ready for negotiations.
Israel and Syria are still technically at war: peace talks broke down four years ago over the future of the Golan Heights which were captured from Syria in the 1967 war.
A proposal to return the land to Syria is supported by two leading Israeli cabinet ministers - Finance Minister Binyamin Netanyahu and Foreign Minister Silvan Shalom.
Talks that were leading Israel to agree to partially return the Golan Heights plateau to Syria broke down in January 2000 after a deadlock.
Washington has threatened Damascus with diplomatic and
economic sanctions, accusing it of sponsoring terrorism and
developing weapons of mass destruction.
Despite this, Damascus is continuing to urged the US to use its influence with Israel to push for a resumption of the Syrian peace track.
Israel's Health Minister Danny Naveh echoed the demand to Syria on Israeli radio on Sunday.
"We would be happy if Syria rejoined the peace camp, but to
start peace talks with Israel it must halt its support for Hezbollah and for Damascus-based Palestinian terrorist organisations," he said.
But a Syrian Government newspaper said that Israel's demands were unreasonable.
"Sharon, who claims to want to resume negotiations without
preconditions, has this time set out irrational and totally
unworkable terms," Tishrin said in its Sunday edition.