The US does not yet have a "complete strategy" for helping Iraq regain territory from Islamic State (IS), President Barack Obama has said.

He said the Pentagon was reviewing ways to help Iraq train and equip its forces.

But Obama said a full commitment to the process was needed by the Iraqis themselves.

He had earlier met Iraqi Prime Minister Haider al-Abadi on the sidelines of the G7 summit in Germany.

IS has recently made gains in Iraq despite US-led coalition air strikes.

In May the militants seized Ramadi, the capital of Anbar, Iraq's largest province, as well as the Syrian town of Tadmur and the neighbouring ancient ruins of Palmyra.

US officials cited a lack of training as a major factor in the fall of Ramadi.

But Obama said that the 3,000 US service personnel in Iraq sometimes found themselves with "more training capacity than we've got recruits".

"We don't have, yet, a complete strategy, because it requires commitments on the part of Iraqis as well about how recruitment takes place, how that training takes place," Obama told a news conference.

The Iraqi government is turning to Shia militias to hold back the IS advance. Photo: AP/BBC

"We want to get more Iraqi security forces trained, fresh, well-equipped and focused and Abadi wants the same thing so we're reviewing a range of plans for how we might do that."

He said it was important to draw Sunni Muslims into the fight against IS.

"We've seen Sunni tribes who are not only willing and prepared to fight Isil [IS], but have been successful," he said.

"But it has not been happening as fast as it needs to."

President Obama said although IS remained "nimble, aggressive and opportunistic", he was "absolutely confident" it would be driven out of Iraq. He said Abadi needed the support of the international coalition as well as a government that represents all the Iraqi people.

He said all countries in the coalition were ready to do more to help train Iraqi security forces.

Earlier, UK Prime Minister David Cameron said Britain was sending an extra 125 military trainers to Iraq.

Last month, US Defence Secretary Ashton Carter said the loss of Ramadi was partly due to the Iraqis' lack of a "will to fight".

Iraq has become increasingly reliant on Iranian-backed Shia militias to take on IS in recent months.

The move has raised fears of worsening sectarian tensions as the militias try to drive the jihadist fighters out of predominantly Sunni areas like Anbar.

President Obama faced strong criticism last year for saying the US did not have an overall strategy for fighting IS, and some US Republicans say IS is benefiting from muddled thinking in the White House.

"We aren't winning the fight against Isil because we don't have a winning plan," Republican Representative Kevin McCarthy said.

On Monday, the Pentagon said Iraqi forces and Shia militias were "making progress" in the battle for the city of Baiji and its nearby oil refinery.

Col Steve Warren said "friendly forces" were in the city and "beginning methodically to root out the enemy".

He said "progress" was also being made at the refinery.

Control of the oil refinery - Iraq's largest - has changed hands several times in recent months. Baiji's capture is seen as crucial for plans to attack IS in the city of Mosul, because of its position on the main road north from the capital Baghdad.

IS overran Mosul, Iraq's second largest city, as it swept across northern Iraq in its June 2014 offensive.