According to Peres, "Halting the activities of terror headquarters in Damascus and stopping Khaled Mashaal's activities in Syria are preconditions for a dialogue as far as we are concerned."
Peres added, "The Syrian desire that Israel would agree to the continued supply of weapons to Hizbullah is an intolerable precondition. We could similarly invited the leader of the Syrian opposition, Khaddam, and equip him with missiles to fire on Damascus."
In an interview with the Lebanese Daily Star on Saturday, Moallem echoed his sentiments of peace, portraying Syria as a potential partner in stabilizing the region.
He referred at one point to "the noble cause of peace between Syria and Israel."
He emphasized Syria's willingness to enter negotiations without preconditions, stating that "a constructive dialogue has to start without preconditions."
Knesset Member Danny Yatom (Labor) called on the government to accept Syrian Foreign Minister Walid Moallem's call for negotiations with Israel without any preconditions, saying that rejecting the call "could lead to war."
Many other politicians also called on Prime Minister Ehud Olmert to seriously consider the proposal.
Yatom added, "I continue to call on Prime Minister Olmert to take leadership and accept Syria's peace challenge. The State of Israel must not reject a proposal for negotiations without preconditions.
"The problem of terror and wars in our region can only be solved through negotiations. Rejecting the Syrian call may lead to an unnecessary war between Israel and Syria, and terror may be enhanced."
MK Ran Cohen (Meretz) welcomed the declaration: "I see it as important progress for peace negotiations. We have reached an absurd situation, in which Syria is going out of its way to signal to Israel about how serious it is, while the Israeli leadership is going out of its way to prevent any progress."
'Recognize Syrian sovereignty over Golan Heights'
MK Ophir Pines-Paz (Labor) believes that Israel must not ignore the remarks made by Moallem and Syrian President Bashar Assad.
"I call on the prime minister, in light of the two Syrian declarations by the president and the foreign minister, not to continue ignoring the Syrian messages, but to look into them seriously.
"Both proposals are very significant, and the policy of denial and ignorance and failure to look into things does not serve the Israeli interests," he said.
The Council for Peace and Security called to launch negotiations which will end with recognition of the Syrian sovereignty over the Golan Heights.
"Israel must express its willingness to sign a peace agreement with Syria, as part of which it would recognize the Syrian sovereignty over the Golan Heights in exchange for peace and security arrangements.
"As part of these changes, Syria will be required to make trust-building moves which will take place during the negotiations. Israel must take moves to examine the seriousness of the Syrian intentions, in coordination with the Unites States," the council announced.
Attila Somfalvi contributed to the report