BAGHDAD — Two suicide bombers described as teenagers carried out attacks Wednesday in suburban Baghdad, killing at least 11, as the prime minister went to the northern city of Mosul to encourage Iraqi soldiers fighting in a new offensive to rid that area of Sunni Islamic extremists.

The Mosul operation follows two other offensives, in Basra and the Sadr City district of Baghdad, that the government has carried out in recent months; the other two offensives focused on Shiite militias.

Iraqi and American security forces believe that Mosul is the last urban stronghold of al-Qaida in Iraq, which American intelligence says is a homegrown militant group led by foreigners.

The Iraqi army began the offensive over the weekend and is being aided by American troops. There has long been support in Mosul for the Sunni insurgency because many former members of Saddam Hussein's security forces live there.

"The goal of this operation is to clean Mosul of the terrorist and criminal groups," said Prime Minister Nouri Kamal al-Maliki, who was accompanied by the ministers of interior and defense. "The operation will open a new page for civilians in Mosul, and the security forces should do everything to make this operation successful just as they are doing in Baghdad and Basra."

Basra has recently settled into relative calm, although it remains unclear if the Shiite militias are finished fighting or simply planning to resume the battle later. Clashes are still going on in Sadr City, although the past few days have been quieter since a cease-fire agreement was reached.

The more damaging of the suicide bomb attacks on Wednesday occurred west of Baghdad about 5 p.m. in Abu Ghraib. It killed at least 10 people and wounded 50, some of them seriously, according to spokesmen for the Fallujah and Jordanian hospitals, both in Fallujah. By nightfall mosques in Fallujah were calling people to donate blood, and police cars were ferrying donors to the hospitals.

The bomber's victims had been mourning the death of Taha al-Zobaie, who was killed two days ago, said Abu Mustapha, a relative who had shrapnel wounds and who would give only his nickname. The Zobaie tribe has opposed al-Qaida in Mesopotamia.

"He was a child about 15 years old, and he was crying," Abu Mustapha said, describing the bomber. "I don't think he exploded himself because I did not see him move his hands. I think someone exploded him by remote control."

The suicide bomb attack south of Baghdad occurred near Yusufiyah, a town that was once heavily dominated by extremists connected to al-Qaida in Mesopotamia. The bomber, who was female, killed an Iraqi army captain and wounded seven Iraqi soldiers, the American military said.

Iraqis in the area described the bomber as being 8 to 12 years old, but an American military spokesman said the bomber appeared to be 16 to 18 years old. The bomber waited four hours for the captain to return to the company's headquarters, telling soldiers there that she needed to talk to him, according to an Iraqi officer who was in the same brigade as the captain. He said al-Qaida in Mesopotamia had put a price on the captain's head.

In Baghdad, the convoy of one of the leaders of the Iraqi Islamic Party was attacked by a car bomb in the predominantly Sunni neighborhood of Yarmouk. The leader, Ayad al-Sammaraie, was not in the convoy, but three of his bodyguards were killed and 23 people were wounded, according to the Ministry of Interior.