Islamic State jihadists can move freely across Iraq's Anbar province and are piling pressure on government forces, despite two months of US air strikes, Pentagon admitted Tuesday.

"It is a tough fight in Anbar," spokesman Colonel Steven Warren told reporters, referring to the unruly Sunni-majority province.

The Islamic State group has pushed back Iraqi government troops in the western province in recent weeks, seizing control of the Anbar town of Heet, west of the capital.

Even before the latest push, insurgents already controlled Fallujah, 50 kilometers (30 miles) west of Baghdad, and much of the desert further west as far as the Syrian border.

"They have relative freedom of maneuver throughout Anbar, and continue to pressure ISF (Iraqi security forces) throughout the entire region," Warren said.

He acknowledged that Asad air base in Anbar province was under threat but said it was up to the Iraqi security forces to prevail against the IS extremists, albeit with the help of US-led air strikes.

"This is Iraq's fight to fight. The Iraqis are holding al-Asad now," he said. "We will continue to use air power as the opportunity presents itself."

Asked if Iraqi forces could fend off the onslaught in Anbar province, he said: "It's hard to say how close Anbar is to falling. It's contested."

There are about 1,400 US troops now in Iraq, including several hundred advisers, but none of them are deployed with Iraqi units in Anbar, Warren said.

The advisory teams are all in Baghdad or in Erbil in northern Iraq.

During the US military occupation of Iraq following the 2003 invasion, the Asad base was a sprawling hub for American forces, including a large contingent of US Marines and a fleet of aircraft and vehicles.

As the IS group pushes towards the main arteries into the Iraqi capital, the chairman of the US Joint Chiefs of Staff, General Martin Dempsey, made it clear that Washington would move decisively to safeguard Baghdad airport, used by US diplomats and troops.

Dempsey said Sunday that American Apache attack helicopters were called in recently when militants appeared to be on the verge of seizing ground just15 miles (24 kilometers) from Baghdad airport.

The IS group was so close that if they had prevailed, "it was a straight shot to the airport," Dempsey told ABC'S "This Week."

"We were not going to allow that to happen," Dempsey said. "We need that airport."

Anbar, largest of Iraq's provinces, is a vast desert area that borders Syria, Jordan, Saudi Arabia and the governorate of Baghdad.