Iraq's interim Prime Minister Ibrahim Jaafari has called for US troops to leave the country soon, but added no timetable had been set for withdrawal.
Mr Jaafari said any withdrawal should be co-ordinated with Iraq
Mr Jaafari was speaking in a joint press conference with US Defence Secretary Donald Rumsfeld, who is in Baghdad on a surprise visit.
Mr Jaafari asked the US to train Iraqi troops faster and to begin handing security control over to local forces.
The top US commander in Iraq has said a withdrawal could begin in the spring.
Gen George Casey, speaking before Mr Jaafari made his comments, said if elections went ahead as planned at the end of the year and security improved, "we will still be able to make fairly substantial reductions... in the spring and summer of next year".
Mr Jaafari said any US withdrawal had to be co-ordinated with the Iraqi authorities.
"We do not want to be surprised," he said.
Mr Rumsfeld urged Iraqis to complete their new constitution on time as he arrived in Baghdad on his unannounced visit.
"Now's the time to get on with it," he said, calling for the committee writing it to meet its 15 August deadline.
Mr Rumsfeld met US troops in Tajikistan before visiting Iraq
He also had strong words for Iraq's neighbours Iran and Syria, who he said turned a blind eye to insurgents crossing their borders into Iraq.
He said Iraqi leaders should insist the two countries "stop foreign terrorists" entering Iraq.
Iraq "should demonstrate that they are a big country, that they are a wealthy country, that they have been around a long time, and they don't like it", Mr Rumsfeld said.
Speaking to reporters as he flew to Baghdad on Wednesday, he said the US would ask the Iraqi government for more people to train as prison guards.
US troops are estimated to be guarding at least 15,000 security detainees in Iraq.
Iraq needs trained guards "so that as soon as it is feasible, we can transfer responsibility for Iraqi prisoners to the Iraqi government", he said.
The writing of the Iraqi constitution has proceeded in fits and starts.
Special efforts were made to include members of the country's once-dominant Sunni minority on the committee writing the document.
Sunni committee members withdrew temporarily after three Sunni politicians were killed on 19 July. They have since ended their boycott.
15 August: Complete constitution
September: National referendum on constitution
December: Elections under new system
Jan 2006: Permanent government takes office
Humam Hamoudi, the chairman of the committee writing the constitution, has said the document will be finished on time.
The committee has the option of extending the deadline for six months, but Mr Hamoudi says that will not be necessary.
He has called an emergency meeting of representatives of the country's various communities and factions to find solutions to the most difficult constitutional questions.
The meeting will take place on Thursday and Friday if enough Sunnis agree to participate, the Washington Post newspaper reported.
Mr Rumsfeld arrived in Baghdad after visiting the Central Asian republic of Kyrgyzstan, where the US maintains a military base to support its operations in Afghanistan.
He was met at Baghdad airport by Gen George Casey, the senior US commander in Iraq.
This is Mr Rumsfeld's tenth visit to Iraq since the invasion in March 2003.
He last visited Iraq in December, when he stopped in Falluja, Mosul and Tikrit on a flying one-day visit.