An explosion on a bus in a Shia district of Baghdad killed 17 people and wounded 41, police said.
Witnesses and the US military said a man wearing an explosives-laden vest got on the bus in the al-Khadamiya neighbourhood and blew himself up.
Earlier, a bomber on a motorcycle attacked mourners at a mosque in Baghdad, killing four and wounding 37.
The mourners were attending the funeral of a woman killed in another bombing nearby on Friday.
The man rode towards a tent full of people and detonated his bomb, witnesses said.
In another deadly attack, a bomber blew up his car at an Iraqi army checkpoint in Latifiya, 30km south of the capital, killing nine Iraqi soldiers, Iraqi officials said.
At least eight bombers staged attacks in and around Baghdad alone on Saturday, targeting religious gatherings and Iraqi checkpoints.
An Associated Press count of the dead from those attacks alone totalled 24, but many more explosions were audible in the capital throughout the day and into the evening.
US soldiers killed
The US military announced that a US soldier died and another was wounded when a bomber blew himself up in Baghdad on Saturday. One Iraqi was also killed, the military said.
Mourners became victims at a
funeral which saw four killed
US military authorities said a US soldier belonging to 1 Marine Expeditionary Force was also killed in a-Anbar governorate.
In other attacks, Aljazeera learned that 25 Iraqis were killed and wounded when a mortar shell fell on one of the Ashura ritual processions in the streets of Silaykh district in northern Baghdad.
Eight Iraqis were also killed and 10 wounded in a car bomb attack on a Shia mosque in Iskandariya town in southern Baghdad.
At a Shia mosque in Baghdad's al-Khadimiya district, four people were wounded in shooting at another funeral, police said.
Shia leaders have repeatedly urged the faithful not to retaliate over the violence, which many fear is specifically intended to provoke a civil war.
Saturday's bombings came despite stepped-up security around the country.
Police secure the area where a
bomb exploded in Baghdad
Authorities had hoped to prevent a repeat of last year's attacks during Ashura in which at least 181 people were killed in twin blasts in Karbala and Baghdad.
Security was tight in Karbala and no attacks were carried out in that city, 80km south of Baghdad.
A sea of people estimated by journalists to be more than 100,000 paraded through Karbala amid intense security.
Tens of thousands more marched to Shia shrines in Baghdad, chanting, beating their breasts and crying "al-Husain" in honour of the Prophet Muhammad's grandson, whose death in battle at Karbala in 680CE is commemorated at Ashura.
Police said local residents helped set up checkpoints in Karbala, where Ashura is most intensely marked. Traffic had been banned around the city to limit the threat of car bombs.
Earlier in the day, a car bomb killed a member of Iraq's National Guard and a civilian in the northern city of Baquba, a National Guard official said.
Shia Muslims flagellate
themselves during Ashura
The blast at the Iraq National Guard headquarters in Baquba wounded one National Guard and three civilians, he said. The driver of the car was also killed in the explosion.
The US military immediately sealed off the area.
A police officer said the bomber arrived just after the Diyala province army commander entered the base.
"General Hid Ayad went through the checkpoint, followed a little later by a Chevrolet, which the driver detonated," said Anas Karim, who was stationed opposite the headquarters.
Four civilians were killed during clashes between fighters and US troops just south of Baghdad overnight, a police official said on Saturday.
The fighting occurred in the town of Haswa, where the fighters attacked a US base, he said.
Separately, two Iraqis were killed and 20 wounded in a mortar attack close to a mosque in Baghdad's Sunni district of al- Adhamiya, medical sources said.
"We have received two dead," said a doctor at the nearby al-Nur hospital.
A bomb attack on a bus killed 17
and wounded at least 41
"Twenty people were wounded when three mortars landed," an interior ministry source said.
Police said the mortar rounds fell close to al-Nida mosque
Near Kirkuk, north of Baghdad, a prominent Kurdish religious
figure, Shaikh Muhammad Rustum Abd al-Rahman, was killed along with his wife by armed men who attacked their car, police said.
In Samarra, also north of Baghdad, two people died and five
were wounded in clashes between fighters and Iraqi soldiers.