Standing alongside Angela Merkel, the German Chancellor who was on a visit to Jerusalem, Olmert insisted Israel had no desire to see a fresh conflict in the region.
"Israel is not planning an attack and does not wish for war, as it did not want one in the past," he said.
Olmert's comments followed a briefing given to the Israeli cabinet earlier on Sunday by Amos Yadlin, the military intelligence chief, in which he set out his assessment of the likely reactions of Iran's main regional allies, Syria and Hezbollah, to an intensifying confrontation between Tehran and Washington.
"They fear a war initiated by the Americans because they understand that there might be an attack against Iran over the summer, but not by Israel," a senior government official quoted Yadlin as telling cabinet ministers.
Although Yadlin insisted that Israel had no intention of becoming embroiled in such a conflict, he warned that any moves by the Jewish state could be wrongly interpreted by its neighbours as a sign of hostile intent.
"If the Americans launch an offensive in Iran, Hezbollah and Syria will think the move had been co-ordinated with Israel and would expect Israel to strike them too," another government official at the meeting told AFP.
Yadlin said he was concerned that the region might inadvertently stumble into a new conflict.
"We might again find ourselves in a war no one wanted," he told ministers. "Israel must be prepared and make sure its steps will not lead to any miscalculation on the other side.
"The new government should show signs of maturity and responsibility"
Husky, Ottawa, Canada
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"Israel is closely following developments on this front out of a concern that the three players might misinterpret certain steps taken by Israel."
Yadlin said Hezbollah was abiding by a UN-brokered ceasefire in south Lebanon, but charged that the Shia fighters were busy rearming north of the Litani river - out of the jurisdiction of UN peacekeepers.
Israel fought a 34-day war against Hezbollah last summer after two soldiers were captured in a cross-border raid.
Around 1,200 Lebanese, mostly civilians, and 160 Israelis, mostly soldiers, died in the conflict.
"Hezbollah has no intention of getting into a second round of conflict," Yadlin was quoted as saying.
"But it is busy rebuilding its forces and has accelerated those efforts for fear of a summer attack."
On Saturday, Iran's joint chief of staff warned Arab states neighbouring Israel against what he called a "Zionist suicide attack" this year.
"The Zionists plan to carry out a suicide plot in the summer," the semi-official Fars news agency quoted major general Hassan Firouzabadi as saying.
He predicted that an Israeli attack would start from Lebanon and Syria and proceed to Jordan, Egypt and Saudi Arabia.