A Syrian state-owned newspaper reported the demand Saturday.
"Barak should adopt a clear-cut policy and deposit a written document to the American side in which he has to reaffirm that his promise to abandon the Golan was not mere talk," Al-Thawra said in an editorial.
According to Israeli media, Barak told his Cabinet no one has asked for such a written pledge, but if anyone did, he would say no.
Barak reportedly said Israel will make a decision on any border adjustments only after it receives satisfactory answers from Syria on security arrangements, water rights, and other issues.
Peace talks between the two nations were to have resumed last week, but were postponed at Syria's request.
Barak reportedly told his Cabinet he thinks the talks would resume soon, but it was not clear precisely when.
Syria has said it will not return to the talks unless Israel is prepared to commit itself to a complete withdrawal from the Golan Heights it captured in the 1967 Arab-Israeli War. Israel has insisted on knowing what sort of security guarantees and peacetime relations Syria would offer in return for a withdrawal.
Meanwhile, Israeli and Palestinian negotiators said on Sunday they would have trouble meeting a February 13 target date for completing a framework deal for a peace treaty.
They also disagreed over whether Israeli Prime Minister Ehud Barak and Palestinian President Yasser Arafat would meet President Clinton in Davos, Switzerland, next weekend at their first three-way summit in three months.
Oded Eran, Israel's chief negotiator with the Palestinians, said the sides had agreed to "expedite and intensify" their talks to try to hammer out a framework accord by February 13 and a treaty by September 13.
"We are now on the 23rd of January and we have three weeks for reaching an agreement if we stick to the original date," Eran told reporters. But realistically, he added, "it's difficult to meet this date."
Also Sunday, a senior PLO official said Arab cabinet ministers attending Middle East talks in Moscow next month will meet ahead of the gathering to coordinate positions on regional cooperation.
"The foreign ministers of Egypt, Palestine, Jordan and ministers from Saudi Arabia, Bahrain, and other states attending the multilateral talks will meet on January 31 in Moscow to coordinate positions ahead of the conference," PLO Executive Committee member Faisal al-Husseini said.
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