Mr Blair, Mr Bush's staunchest ally, briefed the US leader on talks he held earlier this week with Iraq's new Prime Minister Nuri al-Maliki.
The two men, who have seen their popularity ratings drop as a result of the Iraq war, also discussed trade issues, Iran, Afghanistan, and the Middle East peace process.
The prime minister's official spokesman said Mr Blair emphasised "the need for the international community as a whole, including the United Nations, to get behind the democratically elected government of Iraq and support it."
During a press conference after the meeting Mr Bush refused to set a timetable for the withdrawal of US troops from Iraq, saying "we will keep the force level there necessary to win".
The Bush administration has repeatedly stressed that US troops can only leave Iraq when the country's forces can assure security unaided.
Mr Bush and Mr Blair hope to chart a new course following the formation of a new Iraqi government under the country's new prime minister.
Press conference
US and British officials are relying on the new government in Baghdad to help extricate them from an increasingly unpopular war that has left them weakened at home and which is costing both governments billions of dollars each month.
The Iraq venture has also had a higher than expected death toll. In addition to the tens of thousands of Iraqis believed to have been killed since the 2003 invasion to topple Saddam Hussein, Washington has lost 2,460 soldiers and Britain has lost 111.
The United States has about 130,000 soldiers in Iraq. Britain has the second largest contingent, some 8,000 troops.
As the death toll rises, both Mr Blair and Mr Bush have seen their popularity ratings drop. Both need to show their constituencies that there is some movement forward in Iraq, observers say.
Mr Bush, whose popularity has sunk to 31 percent, is also seeking to minimise Iraq war fallout ahead of legislative elections in November that could hurt his Republican Party.
There is speculation that Mr Blair's trip could be his last to the United
States as prime minister, especially after the drubbing his Labour Party suffered in local elections earlier this month and mounting calls for him to step down.
Mr Blair, prime minister since 1997, has pledged to resign before the end of his third term, which is due to expire in May 2010 at the latest.
The two leaders are to meet again Friday after Mr Blair delivers a speech on foreign policy at Georgetown University.