The US military says it is encouraged by a radical Iraqi cleric's order that his Mehdi army militia should freeze operations for six months.
The US says Moqtada al-Sadr's Mehdi army is a big threat to peace
If the freeze holds, coalition forces will be freer to tackle al-Qaeda in Iraq, US commanders say.
A US statement issued three days after the surprise move by cleric Moqtada al-Sadr said it could mean fewer kidnappings, killings and attacks.
Mr Sadr's Mehdi Army has become a major force in Baghdad and the south.
It is accused of sectarian attacks and in April the Pentagon called it the biggest threat to peace in Iraq.
However, the militia has given conflicting signals on whether US military forces would be covered by the freeze.
A US spokeswoman told the BBC that such contradictory signals were unfortunate and worked towards unravelling the prospect of progress.
But hours before the US statement, at least three Mehdi Army supporters were taken from their homes in a raid by US forces in the Shia stronghold of Sadr City.
A militia official said the three were not members of the group, and he believed the Americans had carried out the raid to provoke the Mehdi Army and see how they reacted.
In other developments:
- UK general Sir Mike Jackson, the head of the British army during the Iraq invasion, has said US post-war policy was "intellectually bankrupt"
- violence killed 1,773 civilians in August - up 7% on July, according to Iraq government data
On Wednesday, Moqtada al-Sadr ordered the Mehdi Army to halt its activities for up to six months in order to reorganise it.
Founded in the summer of 2003, its membership is now estimated at 60,000
The group takes its name from the Mehdi - a messianic figure in the Shia tradition
The US says Iran has trained, supplied and financed the group
The militia is accused of infiltrating the Iraqi security forces and has been blamed for attacks on Sunni Muslims
He also ordered it to co-operate with Iraqi government forces and exercise "self-control".
The militia - which has about 60,000 members according to an Iraq Survey Group report in December 2006 - has split in recent months into increasingly autonomous factions.
The US says some are trained and armed by Iran.
"Moqtada al-Sadr's declaration holds the potential to reduce criminal activity and help reunite Iraqis separated by ethno-sectarian violence and fear," the US statement said.
"If implemented, Sadr's order holds the prospect of allowing coalition and Iraqi security forces to intensify their focus on al-Qaeda-Iraq and on protecting the Iraqi population," the statement said.
The BBC's Mike Wooldridge in Baghdad says the Americans will clearly not be lowering their guard against the militia and are, in a sense, challenging Moqtada al-Sadr to show that he can control his increasingly fragmented forces.
The Mehdi Army was created in 2003 to protect the Shia religious authorities in the holy city of Najaf.
It has also been linked to many sectarian attacks on Iraq's Sunni Arabs and has frequently clashed with rival Shia militia.