WASHINGTON: US President Donald Trump praised new Iraqi Prime Minister Ali al-Zaidi as a "champion" in a meeting at the White House Tuesday, even as Washington presses Baghdad to curb Iranian influence.

Trump hinted at making major oil deals with Iraq as he hosted Zaidi, a businessman who came to power this year with US blessing after Trump vetoed another candidate.

"We have a fantastic champion, a new champion," Trump said as he welcomed the Iraqi premier to the Oval Office. "He's been a great fighter and a great fan of America."

Trump said he had even decided to hold an unscheduled lunch with al-Zaidi because of their "tremendous chemistry."

The Iraqi's visit comes against the backdrop of renewed military escalation between the United States and Iran. Washington and Tehran are Iraq's main allies but have long fought a proxy war over the country.

Zaidi has vowed to boost Iraq's fragile economy and disarm pro-Iran armed groups that have targeted US facilities.

He said he would not accept any armed groups outside state control once US forces leave Iraq on September 30, when the US-led anti-jihadist coalition's mission ends.

"On September 30th, American forces will leave, and American companies will enter," Zaidi said. "After 30 September, we will not allow any entity to bear arms outside the state."

Zaidi arrived in Washington on Monday for his first international visit since assuming office -- a week-long trip during which he will also meet US officials and representatives of oil companies.

Trump hinted at likely oil deals with Iraq -- a long-time obsession for a leader who earlier this year asserted control over Venezuela's vast reserves after toppling its leader Nicolas Maduro.

"We're going to be doing a lot of deals," Trump said. "We're going to create a lot of jobs for both countries, and we're going to be taking out a lot of oil."

Delicate balance

Zaidi will however have to continue Iraq's delicate balance between Washington and Tehran.

A senior Iraqi politician told AFP on condition of anonymity that even if the current government adopts a more US-friendly path, prioritising the economy, "it doesn't mean that Iraq is turning against Iran."

Last week, Iraq's holy cities, home to Shia Islam's most sacred shrines, hosted a massive funeral procession for Iran's late supreme leader Ali Khamenei, who was killed in a US-Israeli strike on Tehran as the war began in late February.

While some armed groups said they will cooperate with Zaidi, others remain firm in their refusal to disarm.

Iraq's pro-Iran armed groups have seen their political and financial clout increase over the years, and have long called for the withdrawal of American troops deployed as part of the anti-jihadist coalition.

During the Middle East war, they have intervened in support of Tehran, targeting US facilities in Iraq more than 600 times.

Oil-rich Iraq has been trying to move past decades of war and unrest, but it still suffers from poor infrastructure, failing public services, mismanagement and endemic corruption.

Trump, a long-term opponent of the 2003 US-led invasion of Iraq, said that Washington had "attacked the wrong country", implying that it should have invaded Iran instead.

In recent months, Iraq has signed several deals with US companies in the oil and gas sector.

In the United States, Zaidi is expected to sign more agreements, including one to establish a fund into which Iraq will deposit half a million barrels of oil per day in exchange for help to boost the country's electricity supply.

Like other oil producers, Iraq, a founding member of OPEC, was greatly affected by the Middle East war.

It is hugely dependent on oil exports, which make up about 90% of its budget revenues, and the vast majority of its crude travels via the disputed Strait of Hormuz.