They said the troops had failed to fight their way into the town centre and new efforts to resolve the matter peacefully were underway.
There were conflicting reports on the fate of the hostages, originally said to number about 80.
Earlier on Sunday, a Defence Ministry official said police forces, backed by US-led troops, had entered al-Madain, about 30km south of the capital, at 9am and had "encountered severe resistance from the terrorists".
The crisis began on Friday when armed men allegedly entered the town aboard pick-up trucks, seized a number of Shia and threatened to kill them unless other Shia left the town.
Government forces have
surrounded the town
Government forces surrounded the town on Saturday.
On Sunday, government forces recaptured half the town and freed 10 to 15 families held hostage by the armed men, the Defence Ministry official said, adding that the clashes were continuing.
However national security adviser Qasim al-Daud denied later in parliament that any hostages had been found.
"Three posts where hostages were suspected to have been detained have been raided, but unfortunately we have not found any trace of the detainees", he told Iraq's National Assembly.
Shortly after, both defence and interior ministry officials acknowledged that an all-out offensive against the armed men had been postponed.
The defence ministry said it freed
10 to 15 families
"Iraqi forces have already got into part of the town, but were uncertain about forcing their way to the centre by tomorrow morning", said a defence ministry official.
He added that the Association of Muslim Scholars, the main Sunni cleric organisation, was playing the role of mediator to end the situation peacefully.
"Skirmishes are occurring now and again and the ministry intends to wait for the result of the negotiations" before an all-out attack, he added.
According to an Interior Ministry official, the decision to get into the town was postponed till Sunday morning. "Our forces are now near a roundabout on the way to the town (centre)," he said.
"We will do it with the multinational forces helping us because we need their armoured vehicles," he added.
"We have not found any trace of the detainees"
National security adviser
The hostage-taking in al-Madain has sparked fears of wider
sectarian strife between Iraq's Shia majority and the Sunnis at a time when leaders from both communities are seeking agreement on the make-up of a government.
Officials suggested events in al-Madain might be part of tit-for-tat kidnappings between Shia and Sunnis in the area.
Elsewhere, 19 unidentified bodies have been found over the past few days in the Aziziya region, south of Baghdad, some pulled from the Tigris river, Kut hospital told AFP on Sunday.
"The bodies, all men, are difficult to identify because some appear to have been dead for 10 days" and are badly decomposed, according to a forensic doctor at the main regional hospital.
According to Lieutenant-Colonel Salih al-Shimmari, police chief for Aziziya, a region about 80km south of Baghdad, the bodies were recovered in a number of places, some from the Tigris river.
US soldiers killed
Three US soldiers were killed when a marine base came under indirect fire near Ramadi, west of the capital, the military said on Sunday.
Seven service members were injured in the attack on Saturday night, a military statement said. Three were evacuated for treatment. The other four suffered minor injuries, and two of them have returned to duty.
The attackers fled into a nearby mosque and were pursued by Iraqi security forces, the military said. But no attackers were found there.
The identities of the victims were withheld pending notification of their families.
As of Friday, 1549 members of the US military have died since the beginning of the Iraq war in March 2003, according to an Associated Press count.
At least 1179 died as a result of hostile action, according to the US Department of Defence. The figures include four military civilians.