At least 52 people were killed as security forces stormed a Catholic church in Baghdad to free dozens of hostages, said Deputy Interior Minister Maj Gen Hussein Kamal.
He suggested six attackers had also died in the fighting, though other sources have said the overall death toll was lower.
About 100 people had been inside Our Lady of Salvation for an evening Mass.
The gunmen had reportedly demanded the release of jailed al-Qaeda militants.
The local TV station, al-Baghdadiya, said it had received a phone call from someone claiming to be one of the attackers, who said they were from the Islamic State of Iraq, a Sunni militant umbrella group to which al-Qaeda in Iraq belongs.
Reports said the attackers were not Iraqis, but foreign Arabs.
'Priest immediately killed'
Residents of Baghdad's Karada district, where the attack took place, first heard a loud explosion at about 1700 (1400 GMT) on Sunday, followed by gunfire.
Police said a group of armed men began by attacking the Iraq Stock Exchange building, and then took over the Catholic church just across the road, clashing with guards and killing some of them.
It seems the church was the attackers' real target, says the BBC's Jim Muir in Baghdad.
One eyewitness, who was inside the church, said the gunmen "came into the prayer hall and immediately killed the priest". The witness, who declined to give his name, said worshippers were beaten and herded into an inner hall.
There was a long stand-off as security forces surrounded the building with helicopters hovering overhead.
The militants made contact with the authorities by mobile phone, demanding the release of al-Qaeda prisoners and also of a number of Muslim women they insisted were being held prisoner by the Coptic Church in Egypt.
But the discussions got nowhere, our correspondent says, and the security forces stormed the church.
Witnesses nearby said they then heard two explosions from inside the church and more shooting. The gunmen reportedly threw grenades and detonated their suicide vests.
Maj Gen Hussein Kamal said 52 "martyrs" had died in the fighting, along with six attackers, though a police source earlier said 37 people - worshippers, security forces and attackers - had been killed.
That source said 56 people had been wounded.
Suspects detained
The Iraqi defence minister, Abdul-Qadr al-Obeidi, said security forces approached the building at ground level and from the air.
"We took a decision to launch a land offensive, and in addition an airdrop, because it was impossible to wait - the terrorists were planning to kill a large number of our brothers, the Christians who were at Mass.
"So the operation was successfully done. All terrorists were killed. And we now have other suspects in detention," Mr Obeidi said.
Witnesses say they saw US troops on the ground and US military helicopters hovering above the scene, but the extent of their involvement is not yet clear.
Many churches have been bombed in recent years - including Our Lady of Salvation in August 2004 - and priests kidnapped and killed, but there has never been a prolonged hostage situation like this before, our correspondent says.
There are about half a million Christians from ancient denominations in Iraq.
Iraqi Christians have been leaving the country in droves since the US-led invasion in 2003.
