Prime Minister Tony Blair has said the G8 summit must come up with a plan to de-escalate the Middle East crisis.
Mr Blair blamed Iran and Syria after a meeting with Mr Bush
Mr Blair, speaking after talks with US President George Bush, said G8 leaders must "work very hard to find a common and unified position" on the situation.
The latest violence has dominated the meeting in St Petersburg, Russia.
Mr Blair said that countries such as Iran and Syria "do not want this process of democratisation and peace and negotiation to succeed".
He added he was confident the leaders attending the meeting could agree a position on the situation because they had a "common position in supporting Lebanon in its democracy, in supporting the security of Israel, in supporting the concept of a two state solution".
In an interview for BBC One's The Politics Show, Mr Blair said: "Though this is a difficult thing to say, and I think it has to be said, I don't think anybody really believes that this is just about Hezbollah and Israel.
"We are very worried about the influence of both Syria and Iran in respect of this and that the only way we are going to get a calming down, a ceasefire, restraint shown on all sides is if we deal with the underlying conditions which are the reason why this conflict between Israel and Hezbollah has come about".
Early on Sunday, Israel began a fifth day of bombardments in Lebanon as part of an operation that followed Hezbollah's capture of two Israeli soldiers. Hezbollah has also launched rocket attacks on northern Israel.
Mr Bush said: "Our message to Israel is defend yourself but be mindful of the consequences, so we are urging restraint."
Ahead of the talks, Mr Blair and his wife Cherie joined leaders from Russia, the US, Canada, France, Germany, Italy and Japan at an informal welcoming dinner on Saturday night.
Mr Blair hopes the summit will not just be a "talking shop"
Mr Blair is also set to discuss the Middle East with United Nations Secretary General Kofi Annan on Monday, the final day of the three-day summit.
Oxfam's Jo Leadbeater warned violence was getting worse in Darfur in Sudan, despite G8 pledges to support peacekeeping efforts.
"This meeting is happening against a backdrop of rapidly deteriorating humanitarian crises which the G8 leaders must not turn their back on," she said.
Progress on Africa
Trade in Africa, security issues like Iran and North Korea and Russian democracy are all expected to be discussed on Sunday.
The following day the prime minister is due to make a presentation to fellow leaders on the progress made on pledges regarding Africa at last year's summit, which was held at Gleneagles in Perthshire.
Mr Blair has already said he would not try to bring countries into line with the Kyoto Protocol on climate change.
The G8 countries will be joined by delegates from nations including India, China, South Africa, Mexico and Brazil.
Anti-globalisation protests are also expected, with more than 1,000 demonstrators reported to be preparing to make their voices heard, though they will be kept miles away from the leaders.
Meanwhile President Putin of Russia has taken a swipe at Mr Blair over the UK's criticism of the state of Russian democracy.
Asked by a British reporter for his response to London's disappointment, Mr Putin told a news conference: "It will be interesting for us to hear your experience, including in connection to Lord Levy."
The Labour Party fundraiser who was arrested last week is not exactly a household name in Russia, says BBC correspondent Matt Frei.
He says the remarks have deepened the diplomatic faultlines at a time when the G8 leaders are frantically trying to thrash out some common language on the crisis in the Middle East.
Mr Blair later said he doubted the issue of party fund-raising would be discussed at the summit.