Specter said Israel will have to return the Golan Heights for peace, adding that the United States has the potential to ''bridge the gap'' between Israel and Syria, who have not held peace talks since 2000.
Specter, a Republican from Pennsylvania, and Rep. Patrick Kennedy, a Rhode Island Democrat, held talks with Syrian President Bashar Assad on the last day of their two-day visit to Damascus.
Specter said he had the impression from the meeting that the time was very ''positive for productive talks between Israel and Syria.''
''There is a sense that he (Assad) is ready and the Syrian public opinion is ready (for peace),'' Specter said.
The atmosphere is ''very different in Damascus today and is very different in Jerusalem today'' in part because of last month's US-sponsored Middle East peace conference in Annapolis, Maryland, which Syria attended, Specter said.
In 2000, formal US-sponsored Israel-Syria talks neared agreement but broke down over final border and peace arrangements. Syria demands the full return of the Golan Heights.
''I think it is fair and accurate to say. If there is no Golan return, there is no (peace) deal, that is the core of the deal,'' Specter told a news conference before leaving Damascus.
Assad told the two congressmen that Damascus ''looks positively toward any act that might lead to real peace'' because peace is its strategic choice, Syria's official news agency SANA reported.
Specter, who held talks Saturday with Syrian Foreign Minister Walid al-Moallem, declined to confirm reports that he would convey a message to Assad from Israeli Prime Minister Ehud Olmert on resuming peace talks between the two countries.
Kennedy said he raised the issue of human rights with Assad. The Syrian president said his country only imprisons opposition figures who are linked to foreigners and promised to release members of the so-called ''Damascus Declaration,'' Kennedy said. The declaration was signed by a group of Syrian and Lebanese intellectuals who urged the Syrian government to improve ties with Lebanon, a sensitive issue in Syria.
Relations between Syria and the US appeared to warm briefly following Syria's attendance at the Annapolis conference.
But both sides have since lashed out at one another, each accusing the other of meddling in Lebanon, where the Western-backed government is locked in a political standoff with the pro-Syrian opposition. The US also disapproves of Damascus' support for anti-Israel militant groups and its alliance with Iran.
Last week, US President George W. Bush rejected dialogue with the Syrian leader, saying his ''patience ran out on President Assad a long time ago.''