Blair's Labour Party won in Britain's national elections, but exit poll projections indicated his party suffered a sharply reduced parliamentary majority, an apparent rebuke for going to war in Iraq.
Bush, who was leaving on Friday for a five-day, four-country tour of central and Eastern Europe, was expected to call Blair to congratulate him on the victory, White House aides said on Thursday.
Commenting on the lacklustre returns, Blair said: "We will have to respond to that sensibly and wisely."
White House spokeswoman Erin Healy said she had nothing to add to earlier White House wait-and-see reactions to the election outcome.
Widespread anger over Blair's role in the 2003 invasion of Iraq and outspoken support for Bush appeared to have taken a toll, although an improving economy over Blair's eight years was said to have helped his party win an unprecedented third term.
Before the actual vote count, White House spokesman Scott McClellan said he did not want to speculate on what the ramifications of a reduced majority for Blair's party might be.
A reduced majority could pave the way for Blair to be replaced by a Labour Party rival and complicate US-British dealings in Iraq.
Bush had not explicitly endorsed Blair. White House officials cited a practice of not getting involved in election politics of other nations. But Bush made no secret of his fondness for Blair.
McClellan previously said that Blair "has been a good friend of the president and a strong ally in the war on terrorism and we appreciate the partnership".
Bush saw his own November re-election as a vindication of his handling of Iraq, although polls showed widespread doubts among Americans about whether Bush should have gone to war.
Bush (L) and Blair (R) have a
He also publicly expressed satisfaction over Australian Prime Minister John Howard's re-election and the recent vote of confidence in Italian Prime Minister Silvio Berlusconi, while playing down former Spanish prime minister Jose Maria Aznar's defeat.
Like Blair, Howard, Berlusconi and Aznar strongly supported Bush's Iraq policy and sent troops to Iraq.
All drew sharp criticism at home for that support.