Hoshiyar Zebari's comments on Tuesday follow the announcement of Nuri al-Maliki, Iraqi prime minister, on Monday that his forces would take over security in the southern province of Muthanna in July from a British-led multinational contingent.
"The next province that will follow, according to my discussions with Baghdad, will be the province of Maysan," Zebari told a joint news conference in London with his British counterpart Margaret Beckett.
"This will definitely allow British forces there to be redeployed."
Des Browne, Britain's defence minister, in Iraq for a three-day visit, said he would like to see control of Maysan transferred to Iraqi security forces soon.
He did not say which British-controlled province would be transferred to the Iraqis next.
"Three of the four provinces that we have responsibility for have made progress with regard to security. Maysan has been mentioned before as a province which we would like the Iraqi government and the coalition partners to look at with a view to this process sometime soon," he told Reuters in an interview.
Browne said the 150 British troops deployed in Muthanna would "almost certainly not be based in Muthanna" after the transfer, but they would keep "responsible overwatch" on the province. "Exactly how we will deploy our troops is an operational matter," he said.
Beckett said her ministry would decide whether British soldiers would be pulled out of Iraq or redeployed in another province.
Maysan, whose capital Amara is on the Euphrates, borders Iran and is predominantly Shia.
Browne (L) said he wants Iraqi
forces to take charge of Maysan
Western officials have for several months cited it as one of the regions which could be handed over fairly early on in the process of transferring security control to Iraqi forces.
Southern Iraq has been relatively free of the violence gripping the country but the region has witnessed increasing bombing attacks on British troops and civilians. Britain has some 7,000 troops in Iraq.
Zebari said the capability of Iraq's security forces was improving.
"We have our own plans to accelerate this process," he said. "By the end of the year we hope Iraqi forces will be able to take more and more control of the security situation."