Al-Maliki recommended that responsibility for security in southern Iraq should be handed over to local police and soldiers within two weeks.
The British leader's unannounced two-hour visit signals the start of what he hopes will be the transition of Britain's military mission in Iraq to one focusing on economic development.
An economic adviser is expected to be appointed soon to oversee development projects and create new jobs for residents, Brown said.
Basra's vast oil wealth could offer huge growth potential provided security issues are resolved, officials said.
However, there are concerns that Iraqi forces are not ready to fill the security vacuum that is expected when they are given full responsibility for maintaining order across southern Iraq.
Major-General Jalil Khalaf, commander of the Basra police department, acknowledged last week that his forces lack the means to provide security in the region.
A British parliamentary committee said last month that Britain had failed in its original aim of bringing security to southern Iraq, and expressed concern about continued violence in the area.
There has been major clashes in Basra between fighters opposed to the US and UK presence in Iraq as well as among various Shia groups.
With the handover, Britain will relinquish control of the last of four regions of southern Iraq it occupied after the 2003 invasion.
The final British troops stationed inside the city of Basra withdrew to an airport garrison in September.
The 4,500 remaining British troops in Iraq will drop to 2,500 by the spring of next year.
British troops will take up a role Brown has described as "over-watch", a move that will allow Britain to largely end combat operations but remain on standby.
US officials have expressed concerns about the security of oilfields and military transport lines from Kuwait after the handover.