US Defence Secretary Donald Rumsfeld has said he is convinced there will be a handover of security operations in Iraq to local forces as planned.
Rumsfeld has visited Iraq three times since the end of the war
During a day-long visit to Iraq, Mr Rumsfeld also urged the Governing Council to resolve outstanding issues over the transfer of sovereignty.
But he cautioned against early optimism over an apparent decline in attacks on US-led coalition troops.
Earlier he met US administrator Paul Bremer and military commanders.
Mr Rumsfeld heard an upbeat assessment of the security situation.
He began Saturday's trip in
the northern city of Kirkuk before travelling to Baghdad.
The US commander for Kirkuk told him that fewer US troops would be needed as the security situation showed signs of improving.
Meanwhile the top commander in Iraq, Ricardo Sanchez, said the latest US offensive targeting insurgents' cells was yielding results.
Mr Rumsfeld said that was a good sign - but it should not be overemphasised.
"[The Muslim holy month of] Ramadan has just ended, there has been rain in some parts of the country. So I'm not in a position to say that we're on a positive trend line," he said.
Mr Rumsfeld met members of the new Iraqi civil defence corps in Baghdad.
He said he was satisfied that they would be capable of looking after the security of the country.
"I am convinced that the direction that we set from the outset is the right one and that is being executed exceedingly well, and that the security circumstances in the country will be passed over time to Iraqi security forces of various types, and that they will be able to do it," he said before his departure from Baghdad.
Mr Rumsfeld also met the head of the US-installed Governing Council, Abdel Aziz al-Hakim.
The US defence secretary warned Mr al-Hakim that there was a lot of work to be done to resolve sovereignty issues and very little time to do it, AFP news agency reported.
Mr al-Hakim, who also heads the Supreme Council of the Islamic Revolution in Iraq, a leading Shia party, told Mr Rumsfeld that while everyone backed the 15 November agreement on sovereignty, there were still details to be worked out.
Some Shia clerics have objected to US plans, because of their failure to include direct elections before the proposed transfer of power by next June.
Mr Rumsfeld acknowledged it was proving difficult to track down Saddam Hussein aides, believed to be behind the violence.
"The chances of us stumbling on one of the top guys are zero,'' Mr Rumsfeld said in response to a reporter's question in Kirkuk.
It is the third visit to Iraq by Mr Rumsfeld since the overthrow of Saddam Hussein.
It comes at the end of a whistle-stop trip to another US battleground, Afghanistan, and to
Georgia. He had been set to visit Uzbekistan but fog prevented his plane from landing.
In November, the Americans suffered their worst monthly toll of casualties since major combat was declared over on 1 May, losing 79 soldiers mostly in enemy attacks.
The security situation in Iraq has deteriorated since Mr Rumsfeld's last visit in September.
The unexpected ferocity of the resistance in Iraq has prompted the Americans to seek a swifter exit strategy, correspondents say.