"Our message to Israel is, look, defend yourself but as you do so be mindful of the consequences, so we've urged restraint," Mr. Bush said.
World leaders opened their first working session at the Group of Eight summit Sunday, expressing confidence they would emerge with a consensus position calling for peace - despite differing views on who shares the blame.
"The international community must address the root causes" of the violence taking place in the Mideast, Mr. Bush said as the leaders prepared for their first working session at the summit.
"This started because Hezbollah decided to capture two Israeli soldiers and fire hundreds of rockets into Israel from southern Lebanon," Mr. Bush said. "That's the cause of the crisis."
British Prime Minister Tony Blair, sitting with Bush for a bilateral meeting on the summit's sidelines, said everyone is going to work hard to find a common solution. "We all want the situation to calm down," Blair said.
The only way to stop the hostilities, Blair said, is to address the root causes - the extremists backed by Iran and Syria. "We should be able to agree on a position," he said.
French President Jacques Chirac said the G-8 nations would call for a show of moderation of all parties involved and for a lasting cease-fire in the Middle East.
"We share the same views of issues at stake here in the Middle East," Chirac said as he ended a separate one-on-one meeting with Mr. Bush.
Yet Mr. Bush and Chirac have taken different views of the violence. Chirac has questioned whether Israel's response to the capture of its soldiers went too far, while Mr. Bush has placed blame squarely on Hezbollah and the nations that back it and has declined to call for a cease fire.
Israeli warplanes began striking Lebanon after Hezbollah guerrillas captured two Israeli soldiers Wednesday in a cross-border raid into Israel. The bombings continued into Sunday, as Hezbollah fired barrages of rockets ever deeper into Israel.
The death toll rose above 100 in Lebanon, and stood at 15 in Israel.
Mr. Bush described the escalation of violence as "a moment of clarification" that should show the world how Hezbollah is disrupting the peace process.
"It is a moment that requires all of us to work together and send a clear message, not only to Hezbollah, but to the Iranians who financed Hezbollah and to the Syrians who house Hezbollah," Mr. Bush said.
But as they began their meeting, Mr. Bush and Chirac tried to present a united front.
Referring to his relationship with Mr. Bush, Chirac said he was pleased that "our approach to problems is relatively similar."
Mr. Bush thanked Chirac for France's leadership in helping pass U.N. Security Council resolution 1559 last year, which demands that Syria withdraw from Lebanon and that militias there disarm - a reference to Hezbollah. Hezbollah has refused to disarm as demanded by the resolution, saying it is a resistance movement.
Mr. Bush said he was confident that other leaders would look to the spirit of the resolution as they deal with the cause of the problems in the Middle East - which he identified as Hezbollah and its connections to Iran and Syria.
Chirac said he and Mr. Bush agreed that U.N. resolutions had to be applied, and that "all forces which threaten and endanger the security, stability and sovereignty of Lebanon must be stopped."
Mr. Bush's national security adviser, Stephen Hadley, said the U.S. was pressing for a summit statement identifying Hezbollah as the main culprit and emphasizing the importance of maintaining a democratic Lebanon.
Italian Premier Romano Prodi expressed caution on a joint statement.
"We are still in the phase where we are exposing our positions, not in a negotiating phase," he said.
The Israel-Lebanon crisis and the nuclear ambitions of Iran and North Korea moved to the top of the agenda for the first G-8 summit to be held in Russia.
"We, the Russian side, regret ... that on the eve of the G-8 ... we see an escalation of the situation in the Middle East," Russian President Vladimir Putin, the summit host, said at a midnight news conference.
Putin had molded this year's G-8 summit to showcase his country's re-emergence on the world stage after a devastating economic collapse in 1998, hoping to focus on energy security, the fight against infectious diseases and education.
However, he failed to win a much-anticipated agreement with the U.S. on Russia's admission to the World Trade Organization, the 149-nation group that sets the rules for world trade. The United States is the only country that has not signed off on Russia's membership in the WTO, and Bush dashed Putin's hopes for getting in now.
Japanese Prime Minister Junichiro Koizumi met with Putin ahead of the summit and asked for Moscow's support on the North Korea issue.
But Putin offered a lukewarm reply, saying that while he understood Japan's position, he hoped the U.N. Security Council would be able to work out the proper response, according to Japanese delegation officials who briefed reporters on condition of anonymity.
By JEANNINE AVERSA