Troop withdrawals expected
The BBC, The Times and The Sun reported on Wednesday that under Blair's new plans about 3,000 British troops – about half the current deployment - will have returned home by the end of 2007.
Currently Britain has about 7,100 troops stationed in around Basra.
The British force is the second-largest foreign contingent of soldiers after that of the United States, which has more than 140,000 troops in Iraq.
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Danish media have speculated that Fogh Rasmussen would use Wednesday's press conference to announce a timetable to withdraw all his country's troops.
About 450 Danish troops are stationed in southern Iraq under British command.
Blair has been a key ally of George Bush, the US president, during the war in Iraq and the expected announcement could cause political problems for the US administration.
Washington is planning to send some extra 21,000 troops into Iraq in addition to the 138,000 already there, in a last-ditch effort to restore security in the country.
Gordon Johndroe, a spokesman for the Bush's administration's National Security Council, however played down British plans, saying that Blair had informed Bush of his plans to withdraw troops on Tuesday morning.
He suggested that Blair's move was a signal of increasing stability in Iraq.
"President Bush sees this as a sign of success and what is possible for us once we help the Iraqis deal with the sectarian violence in Baghdad," Johndroe said.
Peak of 46,000 UK troops deployed for 2003 invasion
Some 7,100 still serving in Iraq, several hundred others on ships in Gulf
132 UK soldiers have died in Iraq since 2003
British operations in Iraq under codenamed Operation TELIC
Troops largely deployed in southern Iraq mainly based in Basra, small number also based in Baghdad
10 soldiers killed in aircraft crash in early 2005, single largest loss of life for British troops
Total cost to UK of Iraq war to date: about $7.8 bn
"While the United Kingdom is maintaining a robust force in southern Iraq, we're pleased that conditions in Basra have improved sufficiently that they are able to transition more control to the Iraqis."
He added: "The United States shares the same goal of turning responsibility over to the Iraqi Security Forces and reducing the number of American troops in Iraq."
Analysts predict further violence
Colonel Bob Stewart, the former commander of British forces in Bosnia, said that while Iraqi troops might soon replace British troops on the streets of Basra, the UK's involvement in southern Iraq was far from at an end.
"The British have decided that in order to get out the precondition is that the 10th Iraqi Army division must be good enough, so they have put an enormous amount of time and effort into training them," he told Al Jazeera.
"The British have always wanted to get out ... but they'll be putting a masssive effort into continuing the training and the training will continue I expect long after the British soldiers have come of the Iraqi streets.
"The British can't withdraw until they feel the Iraqi armed forces are in a position to do the job without support."