One bomb killed 36 people and wounded at least 60 at a market in Al-Sadr City, a Shi'ite Muslim district of eastern Baghdad. The market was crowded with morning shoppers.
Two weeks ago, a car bomb in the same area left 60 people dead.
In the northern oil city of Kirkuk, at least 20 people died when a bomb exploded outside a courthouse. Police said some 50 people were wounded, 30 of them seriously.
Kirkuk is a center of Iraq's oil industry and an ethnically mixed town of Kurds, Arabs, and Turkomans.
Iraq has suffered from an upsurge in bomb attacks in recent months, seemingly aimed primarily at fomenting sectarian strife. The principal targets have been Shi'ite.
Iraqi leaders met on July 22 in a show of sectarian and ethnic solidarity, but the biggest party representing the minority Sunni community, the Iraqi Accordance Front, did not attend.
The top U.S. commander for the Middle East, General John Abizaid, said on July 21 that sectarian violence in Baghdad is now a bigger problem than the insurgency.
However, the scale of the threat still posed by insurgents was underlined in overnight clashes in Al-Musayyib, a town just south of Baghdad. Reports indicate that 15 Shi'ite militiamen and an Iraqi soldier were killed. Dozens were wounded. U.S. troops involved in the gunfight appear to have emerged unscathed.
Correspondents say the battle seems to have been part of a systematic campaign against the militia of the radical Shi'ite cleric Muqtada al-Sadr, which is blamed for much of the sectarian violence sweeping the country.
In the far south, British Defense Ministry officials says British forces on July 22 seized a huge cache of weapons and captured a top militant leader blamed for killing British and Iraqi soldiers. Sajid Badir is the leader of the Al-Basrah wing of the radical Shi'ite militia known as the Al-Mahdi Army. An earlier attempt to capture Badir, six days ago, left one British soldier dead.
(compiled from agency reports)