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Bush issued his call ahead of a visit to Britain, the final stop of a European farewell tour on which he has won support for ratcheting up pressure on Iran over its nuclear program, but he still faced lingering concerns about Iraq war.
He said in an interview with Britain's Observer newspaper that the United States and Britain, Washington's main ally on Iraq, both obviously wanted to bring their troops home but that could only be done "based upon success".
"Our answer is: there should be no definitive timetable," said Bush, adding he was "appreciative" that Brown was in frequent touch about "what he and his military are thinking".
The newspaper described Bush as issuing a warning to Brown, but the White House dismissed that tone, saying there was no disagreement between the United States and Britain on Iraq. It later released a transcript of the interview as clarification and said Iran was likely to figure more prominently in talks.
"There is no daylight between the United States and United Kingdom on the strategy for Iraq," White House spokesman Gordon Johndroe told reporters. "Neither of us are looking for arbitrary timetables, troops will return based on conditions on the ground and will return on success."
Only about 4,200 British troops remain in Iraq, most of them stationed at a base in the south. Britain has indicated it could pull them all out by the end of the year, but with the situation still unstable on the ground, that appears unfeasible.
Bush has a more formal relationship with the British leader than with Brown's predecessor Tony Blair, Washington's staunchest supporter over Iraq. Brown is battling against poor opinion poll ratings and Iraq is a divisive issue in Britain.
After arriving in Britain, Bush and his wife, Laura are to meet Queen Elizabeth and tour Windsor Castle near London on Sunday afternoon before attending a dinner with Brown and holding talks with him on Monday.
Protesters are expected to mass in Windsor to demonstrate against the visit, and will later gather outside parliament for a larger anti-war demonstration.
NEW PRESIDENT
When Brown visited Washington in April he caused a stir by meeting the 2008 presidential candidates before Bush, a sign of how leaders are increasingly looking towards a new president.
The White House was keen to play up the mutual respect of the two men and said they had a lot to discuss, including Iran's defiance of international pressure, climate change, energy policy, and the situation in both Iraq and Afghanistan.
With much of Europe still smarting over the U.S.-led invasion of Iraq, Bush has spent a lot of his trip trying to forge a united front to press Iran to suspend its enrichment of uranium which could be used to build nuclear bombs.
There have been only muted anti-Bush protests, in contrast to the big rallies that marred his previous visits. He was warmly greeted by German Chancellor Angela Merkel, Italian Prime Minister Silvio Berlusconi and French President Nicolas Sarkozy.
Germany, Italy and France all offered support for efforts to prevent Iran from obtaining nuclear weapons and Merkel went a step further, backing more sanctions on Tehran if it refuses the latest request from world powers that it stop enrichment.
"Our allies understand that a nuclear-armed Iran is incredibly destabilizing, and they understand that it would be a major blow to world peace," Bush said on Saturday.
White House officials have described discussions about trade, climate change and other issues as productive but have announced no breakthroughs or major initiatives.
Bush is expected to travel to Northern Ireland on Monday after meeting Brown before returning to Washington.
Photo: Reuters