The US president, in St Petersburg for the G8 summit, has insisted Israel is defending itself against terror and Hezbollah is the root of the crisis.
Lebanon and Israel are reviving old divisions between leaders
George W Bush added that the Israelis had to be mindful of the consequences of their actions, as fresh air strikes and rocket attacks were reported.
French President Jacques Chirac spoke out in defence of Lebanon.
The leaders of the world's eight top economic powers have begun working meetings focusing on energy supplies.
With global energy use likely to increase by 50% in the next 25 years, Russian President Vladimir Putin is keen to convince other G8 members his country can be relied on as a supplier.
But Russia's G8 agenda has already been overtaken by events in the Middle East, the BBC's Steve Rosenberg reports.
With eight of the world's most powerful leaders meeting for talks, he says, they are under pressure to find a way to end the hostilities.
"As a sovereign nation, Israel has every right to defend itself against terrorist activity," Mr Bush said after bilateral talks with UK Prime Minister Tony Blair on Sunday.
G8 SUMMIT: 15-17 JULY
The world's seven richest nations - the US, Japan, Germany, France, Britain, Italy and Canada have met annually since 1975
Russia joined in 1998, turning the G7 into the G8
2006 summit to be held in St Petersburg - the first time Russia has hosted the G8
Energy security, infectious diseases and education are on Russia's agenda
Mid-East crisis, Iran, North Korea and international terrorism are also likely to be discussed
"Our message to Israel is defend yourself but be mindful of the consequences."
The root cause of the conflict, he added, was Hezbollah and its ties with Syria and Iran.
Hezbollah, he said, "was the start of this".
Speaking before the first summit working meeting of the day, France's president said that forces "who jeopardise the security, stability and sovereignty of Lebanon must be stopped".
He urged "the protection of civilians, moderation and a durable ceasefire" in both Lebanon and the Gaza Strip.
Our correspondent notes that working out a common G8 position on the crisis will not be easy with a clear division emerging between the US on one hand, and France and Russia on the other.
President Putin has suggested Israel has ulterior motives in Lebanon rather than simply the return of abducted soldiers.
"We condemn any terrorist act including hostage-taking but we have the impression that besides the return of its abducted soldiers, Israel is pursuing other, wider goals," he said on Saturday.