UK Foreign Secretary Jack Straw has promised full international backing for a government of national unity in Iraq.
Mr Straw was speaking in the Iraqi capital, Baghdad, after meeting political leaders including Prime Minister Ibrahim Jaafari.
Mr Jaafari reaffirmed that the next government would be enlarged to include all the main parties.
Iraqis voted in an election last month, with early results suggesting a lead for the main Shia coalition.
Visiting Basra on Friday, Mr Straw raised the possibility that some UK troops might pull out of one or two of the southern provinces within months.
Correspondents say the UK government clearly hopes Iraq is entering a new phase of greater independence.
On Saturday, a car bomb injured several troops and civilians in Baghdad.
Security officials said the vehicle blew up as an Iraqi army patrol passed by in the south-east of the capital, wounding at least 13 people.
Mr Straw has been holding back-to-back meetings with virtually all the key figures in the Iraqi leadership, including not only the Kurdish foreign minister and president and Shia prime minister, but also representatives of Sunni groups.
Speaking to the BBC on the second day of his previously unannounced visit, Mr Straw said the talks had been encouraging.
"[The politicians] expressed their determination to see the Iraqi security forces continue to be strengthened to fight... terrorism themselves and to establish this broad-based coalition government of national unity which all Iraqi politicians know in their head, if not in their heart yet, has to be the future for Iraq," he said.
Mr Straw said there had been a "dramatic" increase in the number of Iraqi security forces being trained over recent months.
"What is more there is now very great day-to-day, hour-to-hour, co-operation between the coalition commanders and Iraqi commanders in very many of provinces," he said.
"The Iraqi politicians I meet are not pressing the coalition for less action against the terrorists and insurgents but for more action and tougher action."
The BBC's Bridget Kendall, who is travelling with Mr Straw, says any delay in forming a new government could deepen the rift between Shia and Sunni and risk pulling the country apart.