Prime Minister Gordon Brown said on Saturday he wanted to reduce British troop levels in Iraq but he refused to set any timetable for their departure.
Making an unannounced visit to Baghdad, Brown was also expected to seek to build on vastly improved security in Iraq to promote investment.
Britain sent 45,000 troops to take part in the 2003 U.S.-led invasion to topple Saddam Hussein, but only some 4,000 remain at an airport near the southern city of Basra where they are training Iraqi security forces.
"It's certainly our intention that we reduce our troop numbers but I'm not going to give an artificial timetable for the moment," Brown told reporters travelling with him after meeting Prime Minister Nuri al-Maliki.
"The tests for us will be how are we meeting the objectives that we've set. What progress can we show?"
Brown's visit coincides with the Iraqi government's growing confidence in its ability to secure the country.
That was reflected in an agreement this week by Maliki and U.S. President George W. Bush to set a "time horizon" for reducing American forces in Iraq.
It was the closest the Bush administration has come to acknowledging the need for a timeframe for U.S. troop cuts. Bush has long opposed deadlines for troop withdrawals.
Brown's government, whose opinion poll ratings have slumped, is expected to make a statement to parliament next Tuesday on the country's future role in Iraq.
The government announced last October it planned to cut troop numbers to 2,500 from around April this year, cutting back its involvement in a war that is unpopular with many Britons.
But the government delayed the move after Shi'ite militias fiercely resisted an Iraqi military crackdown in Basra province in late March.
