Pressure ... Iraqi Prime Minister Haider al-Abadi says Islamic State militants are “on the descent”. Picture: Michel Euler/AP Source: AP

“Our forces are very much advancing on the ground. But they need more air power and more ... heavy weaponry. We need that,” Abadi told Hagel at the start of their talks in the Iraqi capital on Tuesday.

His request highlighted a disagreement over war strategy between Baghdad and Washington, with the Americans favouring a more limited air campaign until Iraqi forces are ready to hold on to territory and organise major offensives.

Winning ... An Iraqi fighter fires at Islamic State militants. Picture: JM Lopez/AFP Source: AFP

Abadi told Hagel as their meeting began that IS “is on the descent at the moment” and that their capabilities had been weakened.

“We are very thankful for the support that’s been given to us,” Abadi said.

Hagel made an unannounced trip to Baghdad as the United States and its allies ramped up their role in the fight against IS, with plans to expand the training of Iraqi forces.

Caliphate ... Fighters from the Islamic State in a commandeered Iraqi army vehicle in the northern Iraqi city of Mosul. Picture: AP Source: AP

Washington has forged an alliance of Western and Arab countries that has launched more than a thousand air strikes against IS since August 8, after the extremist group seized swathes of territory in Iraq and Syria and declared an Islamic “caliphate”.

The United States plans to double the number of its troops helping government forces to 3100, and on Monday the American commander of the war effort said allies also would send roughly 1500 security personnel.