BAGHDAD—Iraq’s government is grateful to U.S.-allied Sunni fighters but won’t allow them to keep their weapons indefinitely, the prime minister said Saturday, hinting at a more intense crackdown.

In recent weeks, the Shiite-dominated government of Prime Minister Nouri al-Maliki has gone after Sunni fighters. Leaders have been arrested and scores of others have been disarmed and banned from manning checkpoints except alongside security forces.

Al-Maliki’s government has mixed feelings about Sunni tribes that rose up against al-Qaida in Iraq, starting in 2007, and joined the Americans in the fight against the terror network.

The groups, known as Awakening Councils, have helped rout al-Qaida in some parts of Iraq. But Shiite leaders fear the Sunnis’ switch of allegiance is just a tactic, and that they could turn their weapons against the Shiite majority.

The U.S., which put many of the Sunni fighters on its payroll, has urged al-Maliki to incorporate them into his security forces, but the government has been slow to do so.

In a speech to Shiite tribal leaders in Baghdad on Saturday, al-Maliki mixed praise for the Sunni fighters with a warning. He said armed groups, alongside security forces, were tolerated for a limited period because their weapons were “aimed at the chests of the terrorists.”

“So they (the Sunni fighters) deserve our gratitude and the inclusion (into the security forces) because we adhere to a policy that there are no arms but the arms of the government,” he said.

In other developments Saturday, a suicide bomber struck a car bazaar in the oil-rich city of Kirkuk, killing at least five people and wounding at least seven others, according to the U.S. military and Iraqi police.

Among those killed was a senior member of a U.S.-allied Sunni group from nearby Diyala province, said Brig. Gen. Sarhat Qadir, a senior police official in Kirkuk. The bomber also was from Diyala, which has been an insurgent stronghold and is the site of ongoing U.S.-Iraqi military operations, Qadir said.

In the capital, gunmen killed an adviser to Iraqi Culture Minister Mahir al-Hadithi in a roadside ambush. A bodyguard was wounded in the attack along a main thoroughfare in eastern Baghdad, police and hospital officials said.

Two cars were involved in the killing of the adviser, Kamil Shiya, the officials said on condition of anonymity because they were not authorized to speak with the media. One vehicle blocked Shiya’s car and gunmen opened fire from the second vehicle.

Shiya’s death was confirmed by officials at nearby Kindi Hospital.