Top US military officer General Martin Dempsey insisted on Tuesday that Washington still has an important role to play in Iraq, as he landed in the country eight months after the last American troops withdrew.

Dempsey, who met with Iraq's Prime Minister Nuri al-Maliki and army chief of staff Lieutenant General Babaker Zebari, is the highest-ranking American to visit Iraq since the December 2011 pullout.

The chairman of the US Joint Chiefs of Staff said in an interview with AFP that the United States still had a role in Iraq, but under much different circumstances.

"We still retain significant investment and significant influence. But now it's on the basis of a partnership and not on the basis of ownership," Dempsey, who served in Iraq as a commander during the war, said before landing in Baghdad.

Dempsey arrived from Afghanistan, where his C-17 aircraft was damaged by an insurgent rocket attack on the tarmac overnight at Bagram air base, forcing the general to use another plane for his trip to the Iraqi capital.

Asked about the rocket attack at Bagram, Dempsey smiled and shrugged, saying perhaps it was a "lucky shot" by the Taliban.

Dempsey, who was last in Iraq in December 2011, stressed that he came to build a dialogue with his Iraqi counterparts and explore expanding military ties, not to make demands.

And he said he wanted to discuss Iraq's interest in training and military exercises with US forces as well as the possibility of arms sales.

"There may be an odd piece of hardware that comes up," he said. "I know they're very interested in air defence, they're very interested in achieving the ability to defend their skies."

Iraqi officials, notably Zebari, have said that while the country's security forces are capable of maintaining internal security, they will not be able to fully defend the country's borders, waters or airspace before 2020.

The US, which at one point had nearly 170,000 troops stationed in Iraq in the years following its 2003 invasion, now has fewer than 200 soldiers in the country under the authority of the US embassy, charged with helping train Iraqi forces on new military equipment.

The four-star general said he would not press the Iraqi government on reports that it may be allowing Iran to ferry supplies to the Syrian regime, which has been fighting a 17-month uprising, through Iraqi territory or helping Tehran circumvent financial sanctions.

"I don't go to Baghdad with an expectation that the prime minister will change his talking points just because I've arrived in Baghdad," he said.

"I don't intend to ask him specifically about whether they are taking any active role in the Syrian situation."

But he said it was possible that weapons or other supplies could be smuggled across the desert of western Iraq without the knowledge of the Baghdad government.

"It is not inconceivable that there are things going on the western edge of Iraq that the central government may lack knowledge of. That's absolutely feasible," said Dempsey.

"It's also possible that they are using that expanse for some purpose," he said. "I don't know if that's going to come up in my conversation today."

Iraqi officials have repeatedly warned that Al-Qaeda fighters were likely crossing the 600-kilometre (375-mile) border with Syria, and have bolstered border security.

They have also denied helping Iran skirt international sanctions, insisting that any relations with the Islamic republic were public and transparent.

Dempsey acknowledged Iran's influence in Iraq but rejected some analysts' forecasts that Iraq was now firmly within Tehran's orbit at the expense of the United States.

"As a democratic nation and the values that we espouse, I would certainly believe at the end of this process, where dictators and strongmen are replaced by representative government, you have to believe that would eventually work to our advantage in terms of our ability ... to engage with those nations."

But he added: "I'm not going to try to understate the role of Tehran."