Deborah Haynes in Bagdad and Francis Elliott in Basra
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Gordon Brown, on a flying visit to Baghdad and Basra, said today he plans to reduce the remaining number of British troops in Iraq following a drop in attacks, but declined to set a timeframe for their departure.
An Iraqi Government official said he hoped British forces would exit within a year.
The British Prime Minister also agreed with Nouri al-Maliki, his Iraqi counterpart, to set up two teams, Iraqi and British, to study the technicalities of Britain's long-term relationship with Iraq.
The two countries must agree on a legal framework for the continued presence of British troops in Iraq after a United Nations mandate expires on December 31.
Speaking to reporters in Baghdad before jumping on a plane to Basra, Mr Brown said: "It's certainly our intention that we reduce our troop numbers but I am not going to be setting an artificial timetable at the moment."
Conditions for withdrawal hinge on completing the training of thousands of Iraqi police and soldiers in the south and helping the authorities to hold local elections.
Britain is also focused on supporting economic development in Basra and the surrounding areas and handing over the oil-rich city's airport to Iraqi hands. Part of the airport is currently used as the main British military base in Iraq.
On the question of how long British troops should remain in Iraq before their tasks are finished, Ali al-Dabbagh, the Iraqi Government spokesman, said: "I think it won't take more than one year."
With bombings and shootings at their lowest level in four years, Iraqi leaders are growing in confidence at being able to operate without the help of foreign forces.
Britain has just over 4,000 troops remaining in the country, a tiny fraction of the 150,000-strong US force, which is also under pressure to leave.
Mr Maliki gave his first clear indication that he wants US troops to withdraw as soon as possible in a magazine interview published today.
"US presidential candidate Barack Obama talks about 16 months. That, we think, would be the right timeframe for a withdrawal, with the possibility of slight changes," he told Germany's Der Spiegel magazine.
In addition, the Iraqi Prime Minister agreed with George Bush this week to set a "time horizon" for cutting US forces. It was the closest the Bush administration has come to acknowledging the need for a timeframe for US troop reductions.
The new rhetoric comes as Mr Obama, who is visiting Afghanistan, prepares to travel to Iraq as part of a tour around the Middle East and Europe.
As for Mr Brown, he spent the morning shuttling around Baghdad's Green Zone in armoured vehicles to meet Mr Maliki and Jalal Talabani, the Iraqi President.
The Prime Minister also spoke with the top two US officials in Iraq, General David Petraeus and Ambassador David Crocker.
Mr Dabbagh, who attended the meeting with Mr Maliki, said both sides agreed to set up a British and an Iraqi teams to explore the two countries’ long-term relationship. Mr Brown and Mr Maliki are due to meet again in the autumn to discuss progress on this front.
The United States, Britain and all other countries with forces in Iraq are looking to sign bilateral accords with the Iraqi Government on a range of different issues, including the legality of the presence of their troops in the country from next year.
After Baghdad, Mr Brown flew to Basra airport, just outside the southern, port city, which until April was effectively in the hands of Shia militiamen despite British forces relinquishing control of security to the Iraqi authorities at the end of last year.
In late March, Mr Maliki launched an operation, backed by US and British troops, to drive out the militiamen and finally put Basra under government control. The offensive postponed a previously announced plan by Mr Brown to cut British troop numbers to 2,500.
Addressing some 150 soldiers, the British Prime Minister thanked them for their service.
“We are now working with the Iraqi forces to train them up so that they can take over responsibility and we can complete our work here in bringing Basra democracy, security and prosperity,” he said. During his brief stay, Mr Brown met Mohammed al-Waili, the Basra Governor, and other Iraqi officials who travelled to the airport base as the Prime Minister did not venture into the city itself.
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