Among those killed in the Sunday night hostage drama were five women, seven children and two priests, an Interior Ministry official and witnesses said. Ten women, eight children and a priest were among the wounded.
"The latest toll is that 37 of the hostages were killed and 56 wounded," the official said, adding that seven security force members were killed and 15 wounded. He did not specify if any Americans were among the dead.
Five attackers were killed and eight arrested, he said, adding there had been more than 100 worshippers at the Sayidat al-Nejat Catholic cathedral in central Baghdad when the hostage-takers stormed in.
The gunmen had attacked during evening mass after killing two guards at the nearby headquarters of the Baghdad stock exchange.
Iraqi Christians have frequently been the target of violence, including murder and abductions. Hundreds have been killed and several churches attacked since the US-led invasion to oust Saddam Hussein in 2003.
Violence has abated in Iraq since its peak in 2006-2007, but deadly bombings, gunfights and kidnappings are still routine.
The US military officially ended combat operations in Iraq at the end of August, but 50,000 troops still remain in the country.