Two separate attacks took place a day earlier, one in Baghdad and the other in Diyala province, which targeted Iranian pilgrims.
The blast in central Baghdad took place as a group of policemen were distributing relief supplies to Iraqis who had been driven from their homes during the sectarian bloodshed that followed the 2003 US-led invasion.
Iraqi police said at least five children were among the dead.
The second attack occurred near Muqdadiya, 80km from Baghdad, in the northeastern province of Diyala, apparently targeting a group of Iranian pilgrims in a restaurant.
Most of the 64 dead were believed to be Iranians visiting Shia Muslim religious sites in Iraq, police said. More than 60 others were wounded.
The attacks were the latest in a series of bombings that have raised fears of a surge in violence as the US military plans for a full withdrawal by the end of 2011.
Security has improved measurably in Iraq over the past two years, but attacks targeting the police are still common in some parts of the country, including the capital.