Brown, on an unannounced visit to Baghdad, said 1,000 more British troops would leave Iraq before year's end.
The U.K. leader arrived in Iraq Tuesday morning to meet his counterpart and discuss troop levels with senior British, American and Iraqi commanders.
He was to meet later with U.S. Commander David Petraeus before flying to Basra to meet with his forces and military leaders in the oil-rich region in the deep south of Iraq.
"We are prepared to take over security of Basra within two months and we will," al-Maliki said, after the meeting in his Green Zone office. "Basra will be one of the provinces where Iraqi forces will completely take over security."
Brown confirmed al-Maliki's plans and said, "as we move to overwatch, we can move down to 4,500." He spoke at the Green Zone residence of Britain's top commander in Iraq Gen. Bill Rollo.
Brown said any further decision on British troop withdrawals would be made next year.
Troops vacated their last remaining downtown Basra base last month, accelerating calls from the British public to drawdown some forces.
Britain has about 5,500 soldiers based mainly at an air base on the fringes of the southern city of Basra, Iraq's second-largest city, 340 miles southeast of Baghdad.
Brown, making his first visit to Iraq as British leader, was expected to address the Parliament in London next week on the future of Britain's role in the war-torn country.
Brown aims for Britain to focus on economic development as its security role reduces and planned to question al-Maliki on the progress of political reconciliation, a British official said before the meeting, on condition of anonymity because of the sensitivity of talks.
Despite ongoing tensions between rival Shiite factions in Basra, the city had avoided the chaos some predicted would ensue after British troops left their last city center base, the official said.
Britain's defense ministry said rocket and mortar attacks on their base at Basra airport had fallen sharply in the last month, with only a few attempted strikes.
But Karim al-Miahi, the head of the Basra security committee and a member in the provincial council said the British forces' withdrawal from the area, "has had a negative effect on security in the city. Iraqi forces still are not able to control the situation which has deteriorated over the past three weeks. There has been an increase in assassinations of police and religious leaders."
Al-Miahi conceded that, "for the areas around the British base, the situation is more stable. Shelling there has stopped."
Abdul-Maunim Karim, 50, a retired sailor who lives near the presidential palace now vacated by the British, agreed that area there was quieter because the shelling had stopped. "But throughout the city violence remains at about the levels before the British troops left."
Advisers to Brown rejected reports the leader had already decided to withdraw between 2,000 and 3,000 troops by the end of the year, but acknowledged he is studying a range of options.
In other developments:
Following a meeting with Petraeus last month in London, Brown pledged Britain "will discharge its duties to the Iraqi people, to our allies and to the international community."
U.S. and Iraqi authorities have aired concerns that a British drawdown could jeopardize the region's rich oil resources and the land supply routes from Kuwait to Baghdad.
In Washington, Senator Joseph Biden issued a statement clarifying what he said were misconceptions about a nonbinding Senate resolution that passed last week under his cosponsorship.
The resolution calls on the Bush administration to encourage the Iraqi government and parliament to adhere to the country's constitution, which lays out a plan for a loose confederation of regions under a limited central government, leaving the bulk of power with the regions.
"Since then, some political leaders in Iraq have misunderstood the amendment. Instead of working to clear up any misunderstandings about the Senate amendment, the U.S. embassy in Baghdad issued a statement that dangerously mischaracterizes it," said Biden.
He said the amendment, co-sponsored by Republican Senator Sam Brownback, "does not call for the partition of Iraq. To the contrary, it calls for keeping Iraq together by bringing to life the federal system enshrined in its constitution.
"Partition, or the complete break-up of Iraq, is something wholly different than federalism. A federal Iraq is a united Iraq, but one in which power is devolved to regional governments with a limited central government responsible for protecting Iraq's borders and oil distribution.
"It leaves the door open for stronger unity if and when passions cool, as we're seeing in the Balkans. Nor does the amendment call for dividing Iraq along sectarian lines," Biden said, adding that the resolution only calls for Iraqis to implement their constitution.
The U.S. Embassy joined a broad swath of Iraqi politicians - both Shiite and Sunni - in criticizing the resolution, seen here as a recipe for splitting the country along sectarian and ethnic lines.
Biden contested the Embassy's assertion that the resolution could lead to "bloodshed and suffering" in Iraq and charged the Bush administration was "pursuing a fatally flawed policy in trying to create a strong central government in Iraq." Biden is a Democratic candidate for president; Brownback is seeking the Republican nomination.