In a gesture to Syria, Prime Minister Ehud Olmert on Thursday said he is open to "any murmur of peace" from Israel's enemies.

Syria has recently signaled that it would like to reopen peace talks with Israel, which broke down seven years ago. Olmert has rejected the offers, citing Syria's support for anti-Israel militant groups in Lebanon and the Palestinian areas.

In a speech to graduates of an air force pilot's course at a base in southern Israel, Olmert indicated he is softening his opposition. "The state of Israel is open to any murmur of peace from our neighbors and across our borders," he said.

Click here for FOXNews.com's Mideast Center.

"If our enemies genuinely want peace, they will find in us a fair partner, determined to establish relations of peace, friendship and reciprocity," he added.

Olmert's spokeswoman, Miri Eisin, played down the comments.

"He has constantly said that if we see anything different, a glimpse of change, then that would be interesting and could make a difference," she said.

However, Syria continues to support Israel's staunchest enemies — including the radical Palestinian groups Hamas and Islamic Jihad, and Hezbollah guerrillas in Lebanon, she added.

There was no immediate reaction from Syria, where government offices were closed at the beginning of an eight-day holiday.

In recent weeks, Syrian President Bashar Assad has offered to restart peace talks with Israel. The offers came in different forms, including news interviews.

In Jerusalem, U.S. Sen. Arlen Spector, who came to Israel after talks in Syria with Assad, said the Syrian leader has asked him to deliver a message: "Syria is very interested in peace negotiations with Israel." But when pressed about whether there were preconditions, Spector told Channel 10 TV, "it got to be a little fuzzy." He said Israel would have to judge whether the offer was serious.

The recent report for the White House by the Iraq Study Group, led by former Secretary of State James A. Baker III and former Democratic Rep. Lee Hamilton, urged Israel to reopen talks with Syria to help reduce tensions in the Mideast. Israel has rejected the report's conclusions.

In peace talks that broke down in 2000, Israel offered return of all of the captured Golan Heights, a strategic plateau Israel took from Syria in the 1967 Mideast war, but the negotiations foundered on Syrian demands for a foothold on the shore of the Sea of Galilee — a major source of Israeli drinking water — and conditions for peace it would give Israel.

Click here for FOXNews.com's Mideast Center.