WASHINGTON — President Bush and Prime Minister Blair met in Washington this week with the limits of their power on full display and the end of their terms on the horizon.

The war in Iraq dominated Mr. Blair’s meetings yesterday and will again today with members of Congress and with Mr. Bush. He arrived in Washington the same day as the release of a report by the independent Iraq Study Group, which Congress created to assess American strategy and recommend a way forward.

The two leaders leaned on the close American-British alliance and their personal relationship to press ahead with the invasion of Iraq more than three years ago at the risk of international isolation. By taking the risk, both men were left weakened at home, a senior Middle East analyst at the International Institute for Strategic Studies in London, Toby Dodge, said.

“Bush’s and Blair’s legacies are going to be ‘Iraq,’ in big flashing letters,” Mr. Dodge said.

While their personal ties remain intact, policy differences and the deteriorating situation in Baghdad are threatening to unravel Messrs. Bush and Blair’s political relationship.

Mr. Blair, 53, met with key lawmakers yesterday, including Senator McCain, a Republican of Arizona, and Senator Boxer, a Democrat of California, to focus on one of the topics that distances him from Mr. Bush: climate change.

Mr. Bush, 60, has resisted setting strict limits on carbon dioxide emissions, even as he promotes research into cleaner burning fuels and lessening America’s dependence on imported oil.

Mr. Blair “will say that climate change and energy security are different sides of the same coin,” his spokesman, Tom Kelly, said.

After a meeting with Mr. Bush and a joint news conference at the White House today THU, Blair will return to the Capitol for meetings with congressional leaders and a group that includes Senators Clinton of New York and Obama of Illinois, two potential Democratic candidates for president in 2008.

Along with climate change, trade, and Africa, the major topic in all of Mr. Blair’s meetings is the recommendations of the Iraq Study Group led by a former secretary of state, James Baker, and a former House lawmaker, Lee Hamilton.

White House and British officials insist the timing of Mr. Blair’s visit with the release of the panel’s report is a coincidence. Still, analysts said Mr. Blair’s presence will help Mr. Bush temporarily stave off calls for a quick or dramatic change in course in Iraq that may follow the report’s publication.

“Blair is not going to interpret Baker-Hamilton as a mandate to get out of Iraq, and in that sense Bush will find some solace in his meeting,” said Lee Feinstein, a senior fellow at the Council on Foreign Relations in Washington. The continuing violence in Iraq, which has surged since the bombing of a Shiite shrine in Samarra in February, has taken a toll on the political standings of both men.

On November 7, Mr. Bush’s Republican Party lost its congressional majorities in an election that turned in part on public dissatisfaction with Mr. Bush’s handling of Iraq. Mr. Blair’s last visit to Washington followed a defeat in local elections for his Labour Party. Neither leader is likely to see his strategy through to the end. Mr. Bush has a little more than two years left in his term; Mr. Blair retires next year.

Mr. Blair has sought to position Britain as close as possible to America in the war on terror, arguing that this gives him unique access to American decision-making. “Most countries around the world would give their eyeteeth to have that relationship,” he said on a visit to Washington in 2004.

Mr. Blair argues that the solution to Iraq lies in engaging with its neighbors and resolving the Israeli-Palestinian Arab conflict. He set out his “whole Middle East strategy” in a November 13 speech in London. Iran is using the pressure points of conflicts in Israel’s Palestinian Arab territories, Lebanon, and Iraq to thwart American and British efforts to achieve peace, he said.

“It is a perfectly straightforward and clear strategy,”Mr. Blair said.”It will only be defeated by an equally clear one: to relieve these pressure points one by one and then, from a position of strength, to talk.”

The next day, when Mr. Blair gave evidence by video-link to the Baker Commission, he repeated his theme, telling them the route to stability in Iraq lay through peace between Israel and the Palestinian Arabs. A solution there, Mr. Blair’s spokesman Tom Kelly told reporters afterward, would be the “biggest single factor” in winning the support of “moderate Muslim countries.”

Mr. Blair sent his senior foreign policy adviser, Nigel Sheinwald, to Damascus at the end of October to meet the Syrian president, Bashar Al-Assad, and urge him to assist the coalition in Iraq.

Mr. Bush has been reluctant to draw Iran and Syria into the discussions, linking Iran’s entry to its compliance with international demands on its nuclear program and Syria’s to that nation halting what America says is its interference in Lebanon.

“Blair now understands that something significantly different will have to be done in Iraq,” an America-Europe analyst at the Center for Strategic and International Studies in Washington who is writing a book about Messrs. Bush and Blair’s relationship, Simon Serfaty, said.