World leaders at the G8 summit endorsed a watered-down version of a US proposal on democratic and economic reforms in the Middle East and North Africa.
Bush had to take account of European concerns
The leaders, meeting in the US state of Georgia, said the reforms should be accompanied by support for a settlement in the Palestinian-Israeli conflict.
President Bush's original plan was seen by the Arab leaders as an attempt to impose American values on their region.
On Thursday, the summit focus shifts to Africa, discussing debt relief.
The G8 leaders also have plans to train and equip more than 50,000 peacekeepers over the next five years, particularly for deployment in Africa.
US officials said the initiative had grown out of African requests for assistance in ending the civil wars plaguing the continent.
The leaders of the UK, Canada, France, Germany, Italy, Japan, Russia and the US said that ending the Palestinian-Israeli conflict was a priority, but should not be used as an excuse for not seeking reform.
"Our support for reform in the region will go hand in hand with our support for a just, comprehensive and lasting settlement to the Arab-Israeli conflict," the statement said.
The BBC's Jill McGivering in Georgia says earlier drafts of the statement originating from Washington made no mention of the importance of the conflict and proved highly controversial in the Arab world and Europe, and the inclusion will make it more palatable to critics.
And in an attempt to deflect criticism from some Arab leaders, the statement noted that the reform should not and could not be imposed from outside.
MAIN G8 ISSUES
Middle East - Israel / Palestinian conflict and looming Iraq handover are key issues. Bush unveils 'Broader Middle East Initiative'.
Oil prices - Financial markets jittery over fears of new terror attacks and possible disruptions of supply.
Debt relief - Leaders expected to vote to extend debt relief for world's poorest nations.
Global economy - Talks on the state of world economy amid growing recovery after three years of relatively weak performance.
International trade - Discussions on WTO negotiations to remove barriers to international commerce.
"Our engagement must respond to local conditions and be based on local ownership," it said. "Each society will reach its own conclusions about the pace and scope of change."
G8 endorsement of the plan was a top priority for Mr Bush, our correspondent says, mentioning as it does the need for democracy in the Middle East as an important weapon in the war on terrorism.
Many Arabs have been cynical about US motives in the region - and Egypt and Saudi Arabia are shunning the talks altogether.
But newly-appointed interim Iraqi President Ghazi Yawer was in attendance, and pledged to build democracy in Iraq.
"Mr President, I'd like to express to you the commitment of the
Iraqi people to move towards democracy," he said in a meeting with US President George W Bush at the sidelines of the summit.
Wednesday's G8 declaration on the Middle East gives its backing to the new Iraqi government.
G8 SUMMIT: LOCATION AND SECURITY
1 Access to Sea Island restricted to G8 delegates and local residents
2 All traffic on Torras Causeway monitored at checkpoints
3 Boating restrictions in place in some areas around Sea Island
4 G8 delegates not staying on Sea Island are staying in Savannah. Armed coastguards, National Guard troops and helicopters on patrol