Olmert addressed the matter during a meeting of his Security Cabinet, a group of senior government and security officials. The atmosphere has been charged by a recent Syrian military buildup and military preparations on both sides of the border — raising fears in Israel that war could break out.
"Israel does not want war with Syria ... We must avoid miscalculations that are liable to lead to a security deterioration," Olmert said, according to a statement issued by his office. It said he has sent this message to Syria through various diplomatic channels.
The prime minister's office released the statement after senior Cabinet ministers heard military assessments of the situation with Syria. Earlier in the day, Defense Minister Amir Peretz issued soothing statements of his own.
The Israeli military "has to be ready on all fronts, irrespective of intelligence reports on what is going to happen," Peretz told Army Radio. But "we have to relay to the Syrians that our exercises and preparations are a matter of course, and in no way reflect Israeli plans to attack Syria."
Israel must probe any possibility of diplomacy with Syria, Peretz said in a separate interview with Israel Radio.
Olmert has acknowledged that Israel would have to give up the Golan Heights, captured 40 years ago this week during the 1967 Mideast War, as part of any peace deal. Israel annexed the strategic plateau in 1981.
Seven years of fractious peace talks between the two sides broke down in 2000 amid disagreements over the scope of a Golan pullout, and relations have steadily worsened since then.
Syria backed Lebanese Hezbollah guerrillas in their war with Israel last summer. It also supports Palestinian militants waging a campaign of violence against Israel.
After the war, Syrian President Bashar Assad offered several times to renew negotiations. Israeli officials dismissed his overtures as a tactic to ease his regime's isolation in the West.
But in recent days, Olmert appeared to have a change of heart. A senior Israeli official said Olmert was assessing prospects for renewed talks.
It is not clear whether this would be driven by an effort to bolster his standing among the Israeli public, which was badly weakened by the Lebanon war; a genuine assessment that Syria is serious about making peace; or the conclusion that Israel should not, in principle, rebuff peace overtures.
An accord could go a long way toward defusing regional tensions that heated up after the Lebanon war. In exchange for returning the Golan, Israel would likely insist that Syria rupture its ties with Palestinian and Lebanese militant groups, and scale back its alliance with Iran.
Syria has not publicly indicated willingness to do any of these things.
While Olmert spoke of relaying messages to Damascus through intermediaries, there have been no authorized direct contacts between the two sides, Israeli officials have said.
Earlier this year, however, a former top Israeli Foreign Ministry official and a Syrian-American businessman who claims ties to the Assad regime disclosed they met several times in the two years leading up to the Lebanon war to probe prospects for talks.