"There's a long history in Iraq", Pompeo told reporters, "and we want them to be successful, independent and have sovereignty and not be beholden to any country".
The visit came two days after US national security adviser John Bolton said the United States was deploying the aircraft carrier USS Abraham Lincoln and its strike group to the region as well as a bomber task force because of a "credible threat by Iranian regime forces".
The top United States diplomat met with Prime Minister Adil Abd al-Mahdi and President Barham Salih while on the ground in the Iraqi capital in a roughly four-hour visit, according to the pool traveling with Pompeo.
"We're working together to push back against that threat", Pompeo said at a press conference with Hunt.
"The deployment of the USS Abraham Lincoln Carrier Strike Group and a bomber task force are considered a prudent step in response to indications of heightened Iranian readiness to conduct offensive operations against USA forces and our interests", he added.
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.
The visit to Iraq came after Pompeo canceled a planned visit to Berlin, citing "international security issues".
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The United States has forces in both Iraq and Afghanistan, which neighbor Iran to the west and east, respectively. "Trump had created a freaky situation in which Iran was more sanctioned for abiding by an global nuclear agreement than it was when the US and the West accused it of violating one", he added.
Pompeo would not be specific about the more recent threat information involving Iran, but said he would make the point in his meetings in Baghdad that any attack by Iran or its proxies on American forces in Iraq would affect the Iraqi government too.
He said the United States would continue to apply maximum pressure to Iran and would not allow the country to threaten US interests.
"We've urged the Iraqi government for its own security to get all of those forces under Iraqi central control", Pompeo said.
"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.
Mr Trump a year ago unilaterally pulled the United States out of an global nuclear deal with Iran, but the United Kingdom and other European powers have refused to follow his lead.
Secretary of State Mike Pompeo on Wednesday vowed the United States would ensure Iran can not build a nuclear weapon if Tehran pulls back from an agreement the Trump administration abandoned a year ago.
The United States also officially designated Iran's Islamic Revolutionary Guard Corps as a terror group, which prompted Iran to name USA forces as terrorists as well.