According to the report, Damascus passed the message on to Israel via Turkish Prime Minister Recep Tayyip Erdogan.

According to the newspaper report, the Syrians demand a series of conditions in that message that must be fulfilled before it will commence a peace process, the first of which is the condition that talks will not be held "under fire." The Syrians explained that by "under fire" they do not mean an armed conflict between Israel and Syria, but rather the conflict between Israel and the Palestinians.

Another Syrian condition is that the talks be held publicly, and accompanied by Israeli gestures to assure the Syrians that they are ready to withdraw from all "occupied Arab territories," Al-Akhbar reported.

A third condition, according to the report, is that Israel hold simultaneous diplomatic talks with Lebanon and the Palestinians alongside peace talks with Syria.

However, "knowledgeable" sources told Al-Akhbar that Damascus estimates that the United States isn't interested in Israel holding talks with Syria, and will act to prevent such talks from taking place.

Sources: Israel warned Syria it could pay price for any Hezbollah attack

In contrast to the Syrian peace overtures, Israel has recently conveyed a stern message to Damascus, also via a third party, stating that it would hold Damascus accountable for any Hezbollah attacks, Israeli and European sources said on Friday.

Israel recently conveyed a warning to Syria through a third party that The sources, speaking on condition of anonymity, said the warning stemmed largely from Israeli concerns that the Lebanon-based guerilla group Hezbollah would launch salvoes of cross-border rockets to coincide with any major Israeli offensive in the Hamas-controlled Gaza Strip.

The sources said the message was conveyed in February through at least one European intermediary following the assassination of a top Hezbollah commander and before this month's five-day Israeli operation in the Gaza Strip in which more than 120 Palestinians, many of them civilians, were killed.

After the group's senior commander, Imad Mughniyah, was killed in a bombing in Damascus, Hezbollah leader Hassan Nasrallah threatened Israel with "open war".

Shi'ite Muslim Hezbollah and its main backer, Iran, accused Israel of being behind the assassination, a charge Prime Minister Ehud Olmert's office denied.

A European source familiar with the matter said the message conveyed to Damascus said Syria could be targeted by Israel even if Hezbollah's attack emanated from Lebanese soil.

An Israeli source with knowledge of government affairs said: "The message was passed around late February, before the last round of fighting in Gaza."

"It has become clear to us Syria has to understand there is a price for its use of proxy terrorism, especially as Damascus is itself a proxy - the long-arm of Iran," the source said.

Another senior government official with knowledge of defense affairs declined comment on whether or not a message had been sent to Damascus, but told reporters that "this is sound strategy. Syria has significantly deepened its involvement with Hezbollah in southern Lebanon since the [2006 Second Lebanon] war."

Asked about the risk of an Israeli attack on Syria in response to a Hezbollah attack, a British official said "there is always a danger that a turn of events here could prompt something on the northern border, which would be a disaster."

"The death of Mughniyah, the threatened Hezbollah retaliation, does leave a specter of a wider regional conflict," the official said, playing down the chances of opening an Israeli-Syrian peace track under the circumstances.

"There's an interest on both sides but I think it's very difficult to move forward on it," the official said, citing close ties between Syria and Iran. "It's become far more difficult the idea of an Israeli-Syrian deal."