Iraqi security forces and allied paramilitaries battled militants from the Islamic State jihadist group in Tikrit on Tuesday, the interior ministry said, a week after the city was declared retaken.

The Iraqi forces launched a raid on the basis of intelligence that there were between eight and 15 IS members in a hideout in the Qadisiya area of north Tikrit, the ministry said in a statement on the day's operations.

"Our security forces were able to kill a number of them while the others blew themselves up after being surrounded," it said.

Prime Minister Haider al-Abadi announced the "liberation" of Tikrit on March 31, but Interior Minister Mohammed al-Ghaban said the following day that "pockets" of IS fighters remained.

The ministry statement shows that operations to fully clear the city are still ongoing.

Bombs also pose a major threat in Tikrit, with Ghaban saying last week that more than 1,000 had already been discovered.

IS led an offensive that overran large areas north and west of Baghdad last June, but Iraqi security forces and paramilitary allies backed by a US-led coalition and Iran have regained significant ground.

The victory in Tikrit is the biggest by Iraqi forces since the conflict began, but it has been marred by allegations of looting and burning by pro-government paramilitary fighters.

IS militants came from the Hamreen mountain range and attacked three checkpoints near the Adhaim dam on Tuesday, which is located some 70 kilometres (40 miles) east of Tikrit, security sources said.

The jihadists struck positions manned by paramilitary Popular Mobilisation forces and police, killing seven and wounding 21, an army colonel said.

He said a colonel from the police's elite SWAT force was among those killed. A medical source and a police major in the town of Muqdadiyah confirmed the toll.

The area of the attack is near the border between the provinces of Salaheddin, of which Tikrit is the capital, and Diyala, which lies to the southeast and which the government said in January had been retaken from the jihadists.

Sporadic attacks have been taking place in several parts of Diyala however and residual IS forces are thought to be hiding in the Hamreen mountains.