Britain, under Tony Blair, the then-prime minister, was Washington's key ally when George Bush, the former US president, ordered the invasion of Iraq.
Following the talks with al-Maliki at Downing Street, Brown said Britain now wanted to get involved in protecting oil supplies from Iraq.
Brown said: "We hope to sign an agreement with the Iraqi government about the future role that we can play in training and in protecting the oil supplies of Iraq and that will be an agreement between our two governments rather than any new United Nations resolution."
Brown said he believed a proposed agreement would go to the Iraqi parliament in the next few weeks.
Al-Maliki has been accompanied on his trip to the UK by several international business people and Iraqi officials to explore possible investment deals with the UK.
Representatives from more than 200 companies, including Shell, Rolls Royce, Barclays Capital and JP Morgan, where Tony Blair works as a senior advisor, are taking part in the meeting.
Senior Iraqi officials including Hussain al-Shahristani, the oil minister, are also attending the day of talks.
Al-Maliki said Iraq needed investment, while Brown said Iraq was open for business and urged British companies to look for opportunities there.
Iraq currently produces nearly two million barrels of oil a day and sits on the world's third-largest proven reserves.
British troop numbers were the second-largest in the Iraq campaign, peaking at 46,000 at the height of combat operations that resulted in the toppling of Saddam Hussein, the former Iraqi president, and his eventual execution for crimes against humanity.
|British troop numbers in Iraq peaked at 46,000 [AFP]
A deal signed by Baghdad and London last year had agreed that the last 4,100 British soldiers would complete their mission, primarily training the Iraqi army, by June, before a complete withdrawal from the country in late July.
By the end of July there will be only around 400 troops left, who will help to train Iraqi troops.
Major general Andy Salmon, the senior British officer in Basra, handed over the southern base to an American commander at a similar ceremony last month, in a key step towards the departure of all foreign troops from the country.
The withdrawal of foreign troops comes amid an upturn in violence in April.
A series of bombings, suicide attacks and shootings have claimed more than 300 lives so far this month.
Under a landmark security pact signed between Baghdad and Washington in November, US troops are required to withdraw from all Iraqi towns and cities by June 30 and pull out from the rest of the country by the end of 2011.
The withdrawal of UK troops comes almost 50 years after Britain's previous exit from Iraq, in May 1959, when the last soldiers left the Habbaniyah base near the western town of Fallujah, ending a presence that dated back to 1918.