BAGHDAD: US led forces have killed 10 Islamic State leaders in air strikes, including individuals linked to the Paris attacks, a US spokesman said, dealing a double blow to the militant group after Iraqi forces ousted it from the city of Ramadi.

Iraqi Prime Minister Haider al-Abadi planted the national flag in Ramadi after the army retook the city centre from Islamic State, a victory that could help vindicate his strategy for rebuilding the military after stunning defeats.

"Over the past month, we've killed 10 ISIL leadership figures with targeted air strikes, including several external attack planners, some of whom are linked to the Paris attacks," said US Army Colonel Steve Warren, a spokesman for the US led campaign against the Islamist group also known by the acronym ISIL.

"Others had designs on further attacking the West."

One of those killed was Abdul Qader Hakim, who facilitated the militants' external operations and had links to the Paris attack network, Warren said. He was killed in the northern Iraqi city of Mosul on December 26.

Two days earlier, a coalition air strike in Syria killed Charaffe al Mouadan, a Syria-based Islamic State member with a direct link to Abdelhamid Abaaoud, the suspected ringleader of the coordinated bombings and shootings in Paris on November 13 which killed 130 people, Warren said.

Mouadan was planning further attacks against the West, he added.

Air strikes on Islamic State's leadership helped explain recent battlefield successes against the group, which also lost control of a dam on a strategic supply route near its de facto capital of Raqqa in Syria on Saturday.

"Part of those successes is attributable to the fact that the organisation is losing its leadership," Warren said.

He warned, however: "It's still got fangs."

"EXCITED ABOUT THIS VICTORY"

The Iraqi army's seizure of the centre of Ramadi on Sunday is its first major victory against the hardline Sunni Islamists that swept through a third of Iraq in 2014, and came after months of cautious advances backed by coalition air strikes.

Three mortar rounds landed about 500 meters (0.3 miles) from Prime Minister Abadi's location during his visit, security sources said. The prime minister was not in danger but was forced to leave the area, they said.

Arriving by helicopter in the shattered city west of Baghdad, Abadi travelled in a convoy of Humvees and met soldiers at the main government complex captured by counter-terrorism forces on Monday, where he planted the tri-colour Iraqi flag.

He had announced the visit to Ramadi himself on Twitter and declared Thursday a national holiday in celebration, even though security forces must still remove explosives planted throughout the city and clear out fighters in some densely built-up areas.

Ramadi was the only city to have fallen under Islamic State control since Abadi took office in September 2014.

"He is excited about this victory, because he managed to remove this blot from his historical record as commander-in-chief of the armed forces," said Hisham al-Hashimi, a Baghdad-based analyst who has worked with the Iraqi government.

The retaking of Ramadi suggested Abadi's strategy of heavy US air support while sidelining the Shi'ite militias could be effective. The militias have served as a bulwark against Islamic State but drawn objections from Washington.

"Ramadi is an example that the regular army wishes to promote for upcoming battles of liberation," Hashimi said.

Coalition spokesman Warren said casualties to Iraqi forces during the battle for Ramadi were in the low double digits. He and Iraqi officials put Islamic State casualties in the hundreds.

Reuters could not independently confirm those estimates.

LONG ROAD TO MOSUL

The government has designated the mostly Sunni city of Mosul, 400 km (250 miles) north of Baghdad, as the next target for Iraq's armed forces.

But Finance Minister Hoshiyar Zebari told Reuters the army would need the help of ethnic Kurdish Peshmerga fighters to retake the largest city under the control of Islamic State, home to rival religious and ethnic groups.

"Mosul needs good planning, preparations, commitment from all the key players," Zebari, a Kurd, said on Monday in Baghdad.

"Peshmerga is a major force; you cannot do Mosul without Peshmerga," he said, referring to the armed forces of Iraqi Kurdistan, an autonomous northern region close to Mosul.