US defence chief Chuck Hagel on Tuesday hailed "steady progress" in the war on the Islamic State group but Iraq appealed for increased military assistance to break the back of the jihadists.

Meeting Hagel in Baghdad, Prime Minister Haider al-Abadi said that Iraqi forces were advancing on the ground against IS fighters who have seized large parts of the country.

"But they need more air power and more... heavy weaponry. We need that," Abadi told Hagel, who was on his first -- and probably his last -- visit to the Iraqi capital as Pentagon chief.

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.

"The focus of our conversations today was the effort to degrade and defeat ISIL (IS), and as I discussed with Iraqi leaders, we are seeing steady progress in achieving this objective," Hagel said.

He said he appreciated Abadi's "directness" in requesting more firepower and added: "We talked about how in fact... the US has accelerated weapons systems that Iraq will need" such as Hellfire air-to-surface missiles and other arms and ammunition.

But Hagel, speaking to a group of US and Australian troops, said the outcome of the campaign would ultimately hinge on the Baghdad government.

"It's their country, they have to lead, they're the ones who are going to have to be responsible for end results," he said. "We can help, we can train, we can assist, we can advise -- we're doing that."

- More coalition troops -

Washington has forged an alliance of Western and Arab countries that has launched more than 1,000 air strikes against IS in Iraq and Syria since August 8, after the extremist group seized swathes of territory and declared an Islamic "caliphate".

Hagel said on Tuesday that four Arab countries -- Saudi Arabia, Jordan, the United Arab Emirates and Bahrain -- had conducted about a quarter of the strikes carried out by Washington's partners in the 60-nation coalition.

US officials have said the scale of the American-led air campaign will not dramatically escalate until the Iraqi army is able to launch wider offensives.

But Hagel also said that Iraqi forces "are preparing now for broader offensives."

Analysts have argued that the next major target for pro-government forces in Iraq would be to start taking back territory in the vast Sunni western province of Anbar, which is under almost total jihadist control.

The United States plans to double the number of its troops helping government forces to 3,100, and on Monday the American commander of the war effort said allies also would send roughly 1,500 security personnel.

Washington has about 1,500 troops in Iraq providing security for the American embassy and advising the Baghdad government's army and Kurdish forces.

Last month President Barack Obama approved the deployment of another 1,500 troops to bolster the training and advising effort across the country.

Hagel announced his resignation last month, rejecting accounts that he had fallen out of favour with Obama as the United States launched a major air war against the IS group.

His farewell tour also took him to Afghanistan and he is due back in the United States on Wednesday.

- IS 'on the defence' -

Hagel flew into Iraq from Kuwait, where US Lieutenant General James Terry on Monday told reporters that members of the coalition meeting last week in the region made initial pledges that would bring "close" to 1,500 additional forces to Iraq to train and assist the country's army.

Terry did not indicate which countries from the coalition would provide the security personnel or how many of them would be in uniform.

He said "the large percentage" of the personnel to be deployed would be training Iraqi troops.

Terry, who oversees the war against IS, said Iraqi security forces were steadily improving but remained months away from staging large-scale offensives that could roll back the militants.

"While they still have a long way to go I think they're becoming more capable every day," he said.

Iraqi counter-attacks against IS are often hampered by homemade bombs planted by the jihadists and Western trainers plan to focus on helping the Iraqis counter the problem, military officers said.

Hagel also addressed complaints by Syria's moderate rebels, who are battling both the jihadists and the regime of President Bashar al-Assad, that foreign help was not forthcoming.

"We are also working closely with regional partners to begin training and equipping the moderate opposition in Syria to defeat ISIL there," he said.