Britain will continue its handover of formal control of security to Iraqi forces in the south of the country, Defence Secretary Des Browne has said.
Mr Browne, in Baghdad for talks with Iraqi Prime Minister Nouri Maliki, said security in the south had improved.
He said it "should be possible" to name a date for transition in Dhi Qar province. This would leave only two provinces under UK control.
His announcement came after a weekend of violence in Iraq left dozens dead.
At least 60 people have been killed in a series of gun battles between soldiers and militias across the country.
On Monday, a suicide bomber killed 11 people near to the interior ministry in Baghdad.
Mr Browne said he recognised there were "continuing challenges" in Iraq.
"I've seen some violence over this weekend which suggests there's much more work to be done," he said.
But he added that "things are improving and the challenge is to maintain that improvement".
Mr Browne revealed he had held talks with his Iraqi counterpart Abdul-Qader Mohammed Jassim al-Mifarji over the security situation in Baghdad.
"We also discussed the minister's plans for extra recruiting and equipment to make Iraqi armed forces stronger and more mobile," he said.
Last month, about 1,000 British troops were withdrawn from a base in Maysan, although the province remains under British control.
The base was looted immediately after it was handed over to Iraqi authorities.
Mr Browne said lessons needed to be learned from that experience, and he would be raising the matter with British Army commanders.
The handover of security arrangements in Dhi Qar is expected to take place next month.
That would leave only the city of Basra, its surrounding province, and Maysan in British hands.
Chief of Defence Staff Sir Jock Stirrup has said control of the city of Basra could be handed to local security forces early in 2007.
BBC correspondent in Baghdad, Mike Wooldridge, said Basra would be "the most problematic handover, given the continuing violence in the city and underlying local power struggles".
There have been 115 British troops killed in Iraq since the 2003 invasion.
Britain currently has more than 7,000 troops in the country.