Tehran had said it planned to cease "some commitments" on its deal.
But Iraq is also host to more than 5,000 US servicemen and women invited by the Iraqi parliament in 2014 to assist in the war against the Islamic State group.
European diplomats urged the United States to exercise "maximum restraint" as tensions mount in the Gulf a year after Washington withdrew from a landmark deal that curbed Iran's nuclear programme.
In a Friday press release, the department announced that Pompeo would leave on Sunday for a two-day trip to Moscow and Sochi, where the State secretary will meet with Putin and Russian Foreign minister Sergey Lavrov.
The official said one primary focus of the meeting would be Trump's desire to modernize and expand existing arms control agreements, particularly ahead of the formal USA withdrawal from the Intermediate Nuclear Forces treaty in August after Washington's repeated complaints that Moscow was violating it. Trump has said he wants new arms control accords that reflect the current post-Cold War situation and bring in other nations, notably China. "That continues to be the case", said Pompeo's top Iran adviser, Brian Hook.
The US has continued to build pressure on Iran, with Pompeo accusing Tehran of planning "imminent" attacks.
Asked if he believed there was the possibility of an Iranian role, Hook had no comment.
Iran says the strategy amounts to "psychological warfare" and a senior Iranian Revolutionary Guards commander on Sunday said Iran would retaliate against any aggressive USA moves.
Russian Deputy Foreign Minister Igor Morgulov said Wednesday that the Democratic People's Republic of Korea would be a topic in the discussion between Lavrov and Pompeo, who have just met in Finland earlier this week during the 11th Ministerial Meeting of the Arctic Council.
Venezuela is only one of a slew of issues where the United States and Russian Federation have clashed.
"Getting along with Russian Federation and China, getting along with all of them is very good thing, not a bad thing". Europe sees it as key to preventing a nuclear-armed Iran, the report said.
"The secretary wanted to share some details behind what we have been saying publicly", Hook said. "We are very concerned about Iran's - a lot of the multiple threat streams that have been reported over the last three or four days".
Iranian President Hassan Rouhani chairs a cabinet meeting in Tehran, Iran, May 8, 2019.
Maas said he had again told Pompeo that Berlin did not want a military escalation.
"What we need is a period of calm to make sure that everyone understands what the other side is thinking", Hunt said, adding that would share those concerns Monday with European partners and Pompeo.
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