Iraq's Prime Minister Haider al-Abbadi has pressed outgoing US Defence Secretary Chuck Hagel for more air strikes and weaponry to accelerate what he called the "descent" of the Islamic State of Iraq and the Levant (ISIL).

Hagel flew in to Baghdad on Tuesday for meetings with Iraqi government officials and American military commanders.

Abbadi told Hagel that ISIL's capabilities had been reduced.

"Our forces are very much advancing on the ground. But they need more air power, more heavy machine guns, heavy weaponry on the ground," the prime minister said.

As Iraqi leaders and the people of Iraq know, only they can bring lasting peace to their country if they are resolved to do that.

Chuck Hagel, US defence secretary

The plea underscored tension in the US-Iraqi relationship, with Baghdad pushing for more aggressive assistance than Washington has provided so far, four months after President Barack Obama launched air strikes against ISIL in Iraq.

US officials assert that the Iraqis' biggest need is competent military leadership, not additional military hardware.

Iraqi forces have strengthened their positions around Baghdad and blocked ISIL's move south, Hagel said. They "will be able to intensify offensive operations as the coalition's training effort expands into northern, western, and central Iraq," he added.

Hagel suggested that success on the battlefield was only part of the answer. He said the key to progress was an inclusive government in Baghdad that could rally all Iraqis - something he said Abbadi was working towards.

"As Iraqi leaders and the people of Iraq know, only they can bring lasting peace to their country if they are resolved to do that,'' he said.

Obama ordered US troops out of Iraq in 2011 but sent some back this summer to help counter the advance of ISIL, which has declared a "caliphate" on territory it has captured in both Iraq and Syria.

Last month Obama authorised roughly doubling the number of ground forces to 3,100 as the military expands the reach of its advisers and starts training the army and Kurdish forces.