Iraqi Prime Minister Nouri Maliki has pledged to tackle illegal militias, which are widely blamed for the growing sectarian violence in the country.
Four people were killed in the raid on Sadr City
He said his forces would strike hard at anyone who defied the law.
But he insisted he was working to his own timetable, not a US-imposed deadline for improving security.
Mr Maliki also said there had been a lack of co-ordination with coalition forces over a raid in Baghdad's Sadr City that resulted in four deaths.
Iraqi special forces went into Sadr City, a stronghold of the Mehdi army militia, overnight to try to capture "a top illegal armed group commander" who directed death squads in eastern Baghdad, a US military statement said.
Iraqi forces came under fire and called for back-up from US aircraft, which used "precision gunfire only to eliminate the enemy threat", the statement said.
But Iraqi police said the US troops shot at them while they were trying to take people injured in the raid to hospital.
At least four people were killed and about 15 injured, provoking anger in Sadr City.
There has been no indication of whether the suspected militia leader was captured.
Relatives and the wounded blamed US forces and the Maliki government, Reuters news agency reported.
"Where is Maliki? Where is his freedom?" one man lying on a stretcher said.
Mr Maliki, speaking at a televised news conference later on Wednesday, sought to distance himself from the operation.
He blamed a lack of co-ordination between Iraqi and US forces, despite a US military statement that said the raid was "authorised by the Iraqi government".
"We will be seeking a full explanation from the multi-national forces," Mr Maliki said.
The Iraqi prime minister pledged to deal with the militias that are blamed for much of the sectarian violence in Iraq.
"We will strike hard at anyone who defies the law or transgresses the authority of the state," he said.
But he denied that the Iraqi government had accepted a US time-frame for curbing the violence.
"I affirm that this government represents the will of the people and no-one has the right to impose a timetable on it," Mr Maliki said.
The BBC's Andrew North in Baghdad said the Iraqi prime minister appeared to be directly contradicting US ambassador Zalmay Khalilzad, who said on Monday that the Iraqi government had agreed to develop a timeline for progress by the end of the year.
Mr Maliki also warned "friendly and neighbouring countries" against meddling in Iraqi affairs.
"Time is running out and we can no longer accept this interference," he said, without naming the countries he was referring to.
On Tuesday, key figures in the Bush administration outlined a series of measures to try to stabilise Iraq, including a plan to reform Iraqi security ministries.
Nouri Maliki seen here with Moqtada Sadr has to tread a fine political line
Mr Khalilzad said he expected "significant progress" within the next 12 months.
He singled out the Mehdi army, saying it must be "brought under control, it has to be decommissioned, demobilised and re-integrated like other militias".
The Mehdi army, a militia linked to Shia cleric Moqtada Sadr that holds sway in much of Sadr City, has repeatedly been accused of involvement in death squads carrying out attacks on Sunnis.
Correspondents say tackling the Mehdi army and other Shia militias is one of the most difficult problems facing Mr Maliki.
BBC Middle East analyst Roger Hardy says the Iraqi prime minister is caught between his American ally and Shia public opinion and has extremely limited room for manoeuvre.
Mr Maliki's fragile coalition government includes Shia parties that have links to powerful militias.