General Ray Odierno, the commanding officer of US forces, said he would push ahead with plans to reduce numbers by the end of August and see a complete pull-out by the end of next year.
"As I look at it today, we think we're on track to be down to 50,000," he said. "There's nothing today that tells us that we don't think the Iraqis will be able to form this government in a peaceful way."
Both Iraqi and US leaders have been relieved at the relatively calm atmosphere in Iraq's major cities before and during the election. The wave of bombings which killed 38 people on polling day on Sunday and several dozen more in the weeks beforehand was not as bad as feared.
Early indications on Monday suggested a close race between the two leading coalitions and the potential for a long stand-off as the winner tries to negotiate with smaller parties to form a government.
But Washington will be heartened at an apparently poorer showing for an Islamist grouping, many of whose members have close ties to Iran and to Shia militias, which had also been expected to compete for the top place.
The Independent High Electoral Commission last night said turnout was 62 per cent, less than the previous general election in 2005 but better than many had expected after years of sectarian street warfare in major cities.
Election officials reported the State of Law coalition of Nouri al-Maliki, the prime minister and pre-election favourite, was ahead in half the country's provinces. Mr Maliki's grouping is largely Shia and although it claims to be cross-sectarian has its power-base in the Shia southern areas.
A victory for either Mr Maliki or the Iraqiya nationalist grouping of former prime minister Ayad Allawi would be regarded as acceptable by the United States.
Iraqiya is expected to dominate the votes of Sunni regions, where turnout was said to be particularly high.
The Shia Islamists of the Iraqi National Alliance were expected to do well in poor areas such as Baghdad's two-million strong, impoverished Sadr city.
This is the power base of the Mahdi army of Moqtada al-Sadr, who has said he is committed to the electoral process but whose candidates include some accused of criminal activity.
Hakim Fadily, once accused of using his position as deputy health minister to carry out killings of Sunni patients and to use ambulances to run guns, said the Mahdis would be willing to take up arms again if necessary.
"I don't expect American troops to leave Iraq," he said. "The American approach is to impose themselves by force and humiliate the Iraqi people."
General Odierno has admitted he has contingency plans to keep troops in place if the situation deteriorates.
Another Shia candidate, Raad Mukhlis, called on America to help the formation of a new government.
"I hope and pray the Americans don't pull out completely," he said. "We didn't invite them to come to our country but since they are here we need them to rebuild it – build a new democracy, not just an election."
General Odierno said that the scores of mortar rounds thought to have been fired at Baghdad on Sunday were probably harmless "bottle bombs".
Mr Allawi's group have complained of "irregularities" at polling stations.
But a spokesman for the United Nations said: "We have an inclination to say that these elections were well organised."