The top US diplomat's unannounced visit marked an effort to stand up Washington's ties with Baghdad as it pushes ahead with its "maximum pressure" against Tehran -- a US arch-rival, but an ally of Iraq.
Pompeo abruptly cancelled talks in Germany and made a lengthy detour from a European tour to spend four hours in Iraq, where he met both President Barham Saleh and Prime Minister Adel Abdel Mahdi.
"We talked to them about the importance of Iraq ensuring that it's able to adequately protect Americans in their country," Pompeo told reporters after the meetings.
Pompeo launches Mideast tour vowing no Islamic State return
"They both provided assurances that they understood that was their responsibility," he said.
Pompeo said he made the trip because Iranian forces are "escalating their activity" and said the threat of attacks were "very specific".
"These were attacks that were imminent," Pompeo said.
He declined to go into further detail on the alleged plot, which has been met with scepticism in numerous quarters, with leading Democratic lawmakers fearing that President Donald Trump's administration is seeking to spark a war with Iran.
In the latest US move, the Pentagon said it was sending several massive, nuclear-capable B-52s to the region.
The deployment was in response to "recent and clear indications that Iranian and Iranian proxy forces were making preparations to possibly attack US forces," the Pentagon said.
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On Sunday, Washington announced it was dispatching an aircraft carrier strike group to the Middle East as national security advisor John Bolton warned Iran that Washington would respond with "unrelenting force" to any attack by Tehran, including by its regional allies.
Iraq's majority population enjoys religious kinship with Iran, which played a significant role in helping Baghdad to fight the Islamic State extremist movement.
President Hassan Rouhani paid an official visit to Iraq in March, where he denounced pressure from the "aggressor" United States, which deposed Iran's arch-enemy Saddam Hussein in a 2003 invasion.
Pompeo, whose trip to Iraq is his second this year, said he spoke at length about Iran's influence with militias.
"We've urged the Iraqi government for its own security to get all of those forces under Iraqi central control," Pompeo said.
"In each of those meetings, those two leaders promised that that was their objective, too, they were moving towards that goal," he said.
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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.
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.
The Trump administration has imposed sweeping sanctions on Iran, including trying to stop all exports of its oil, although it has issued a waiver for energy-starved Iraq to keep buying power from its neighbour.
Iranian media have said that Rouhani will announce retaliatory measures on Wednesday to mark the anniversary of Trump's pullout from a 2015 nuclear accord under which Tehran drastically scaled back its sensitive work.
With the imposition of US sanctions, Iran has grown increasingly frustrated that it has not seen the fruits of the agreement, with which UN inspectors say it is complying.
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.
Germany has wide disagreements with the Trump administration and along with other European nations still supports the 2015 nuclear deal negotiated under former US president Barack Obama.
German parliamentary foreign affairs committee chair Norbert Roettgen said that "even if the reasons for the rejection are unavoidable, it unfortunately fits in with the current climate in the relationship between the two governments".
But Pompeo said that Maas was "most gracious" in a telephone call in which he told him he would scrap the visit.
Pompeo, who returns to Europe for talks Wednesday in London, said he would try to reschedule his trip "as soon as we possibly could".
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