The source, speaking on condition of anonymity because of the high security nature of the visit, said Pompeo was due to meet Iraqi Prime Minister Adel Abdel Mahdi.

The surprise visit is seen as an effort to stand up Washington's ties with Baghdad as it wages a campaign of "maximum pressure" against Tehran -- a US arch-rival, but an ally of Iraq.

On Sunday, Washington announced it was dispatching an aircraft carrier strike group and bomber task force to the Middle East in a "clear and unmistakeable" message to Iran.

National Security Advisor John Bolton said the deployment was in response to a "number of troubling and escalatory indications and warnings," but did not elaborate.

Both Bolton and Pompeo have said in recent days that the US would respond to any attack by Iran, its feared Islamic Revolutionary Guard Corps, or armed groups allied to Tehran across the region.

- 'Security posture' -

Pompeo had been travelling from Finland, where he had attended a meeting of the Arctic Council, to Germany, where he was due to meet both Chancellor Angela Merkel and Foreign Minister Heiko Maas later Tuesday.

He suddenly cancelled the trip due to "pressing issues," the State Department said on Tuesday, without elaborating where he was heading.

But in response to a question about threats from Iran or its proxies on US forces in Iraq, the top US diplomat mentioned both Iraq and Jordan.

"As Secretary of State I have a responsibility to keep the officers that work for me safe each and every day all around the world. That includes in Arbil and Baghdad, in our facilities in Amman, all around the Middle East," he told journalists.

"And so any time we receive threat reporting, things that raise concerns, we do everything... that we can to make sure that those planned or contemplated attacks don't take place, and to make sure that we've got the right security posture," he said.

In a press conference a few hours before Pompeo's arrival, Abdel Mahdi said Iraq would not accept any attack on foreign troops on its land.

"Iraq really is taking the responsibility to avoid any attack on any of our friends here, coalition forces or any of our friends here," he told reporters.

"This is an obligation that Iraq would honour, (and) not accept any attack on anyone -- whether Iraqi, foreigner, whether it's an embassy or a company or a military mission," he said.

Pompeo and Abdel Mahdi had spoken by phone on Friday, but a readout provided by the PM's office did not mention Iran.

- Tit-for-tat -

Pompeo is due in London after his trip to Iraq, his second time in Baghdad as secretary of state.

He travelled to Baghdad and Arbil in January, also unannounced, to reassure Washington's Kurdish allies after the US announced it would withdraw its troops from Syria.

Washington and Tehran have been at loggerheads since the US unilaterally withdrew from the 2015 Iran nuclear deal and instead vowed "maximum pressure" against Tehran -- with Baghdad repeatedly caught in the middle.

In November, the US reinstated tough sanctions on Iran's energy and finance sectors, but granted Iraq waivers to keep importing Iranian electricity and gas for its crippled power sector.

The US has urged Baghdad to partner with US companies to fill that gap.

And last month, Washington named the Iranian Revolutionary Guard Corps a "foreign terrorist organisation," in the first such designation for a government body.

The move prompted Iran to designate US troops across the region as "terrorists."

In Iraq, a debate has been raging in recent months over the fate of some 5,200 US troops stationed across the country.

Their presence angers the Hashed al-Shaabi, a paramilitary force that is dominated by pro-Iran factions which played a key role alongside government forces in the fight against IS.