Gordon Brown has said he favours reducing troop numbers in Iraq but would not set an “artificial timetable” during talks with Iraqi leaders.
The prime minister also met senior US officials during a surprise visit to the country, ahead of a statement next week on Britain’s involvement there.
He said “enormous progress” had been made in Iraq recently and paid tribute to the “resilience” of UK forces.
In Iraq to assess the UK’s goals there, Mr Brown also said violence had fallen.
Mr Brown flew into Baghdad on Saturday for talks with Iraqi prime minister Nouri Maliki, president Jalal Talabani and military leaders.
He also met US military chief General David Petraeus and US Ambassador Ryan Crocker.
He flew on to Basra where he is due to meet British troops and review progress in reconstruction projects.
The UK prime minister said there were four main objectives he wanted to see met in Iraq, including the training of local army and police and the holding of local elections.
He is also focusing on economic and social development in the Basra area, and the transfer of Basra Airport – where most British forces are currently based – to civilian use.
Plans to halve UK troop numbers to 2,500 by spring were delayed due to violence in Basra at the end of March.
Numbers had been reduced from 5,000 to 4,000 between October 2007 and early April.
Military commanders have said they expect numbers to be further reduced during the course of 2009, said the BBC’s Jim Muir in Baghdad.
Speaking after his meetings with Iraqi leaders Mr Brown said: “It is certainly our intention that we reduce troop numbers, but I am not going to give an artificial timetable at the moment.”
Mr Maliki is keen to get a withdrawal timetable in place before the US presidential elections in November.
Meanwhile Liberal Democrat leader Nick Clegg called on Mr Brown to withdraw British troops in southern Iraq and put more into the “increasingly difficult job” of fighting the Taleban in southern Afghanistan.
In a press conference Mr Brown said the number of violent incidents had reduced dramatically since he was last in Iraq December, falling from six violent incidents a day to one every six days.
“Enormous progress has been made,” he said.
“It’s important to recognise that security, prosperity, local democracy – these are the things that we are trying to move forward and trying to achieve.”
He added: “I am very grateful for the way the British forces behaved in such an exemplary manner. Their professionalism, and their courage, and their dedication is very much part of the progress that has happened.”
Mr Brown – whose visit was not announced in advance for security reasons – spent just under an hour in talks with Mr Maliki, then with his advisers. He then spent 20 minutes with Mr Talabani at the presidential palace.
In his last visit in December he announced the official handover of Basra to Iraqi authorities.
This week Iraq and the US called for an agreement on a “general time horizon” for the withdrawal of US troops.
‘Basra another Dubai’
The UN mandate covering foreign troops in Iraq expires at the end of the year.
The US is negotiating a new bi-lateral agreement to cover their continuing presence, and Britain will have to do the same, said Jim Muir.
He said Mr Brown would also be talking to Mr Talabani about the “broader relationship” between the UK and Iraq, with a focus on getting more investment and jobs into the country.
When asked if Britain was motivated by its need for Iraq’s oil, our correspondent said Iraq was “awash” with money from increasing oil revenue.
“The British a looking to play a big development role down in the south… and they are very much encouraging foreign firms to come in and invest, not just in oil but in other projects.
“The British commander down there is talking about Basra being another Dubai in 10 or 20 years down the line, and so there’s huge potential and obviously Britain wants to be part of that effort and obviously to help profit from it as well.”
Mr Brown said he had agreed to hold further talks with Mr Maliki in the autumn.