The change falls short of the withdrawal from the region of non-essential staff presently taking place for US forces, with the State Department confirming Wednesday that it had ordered all non-essential staff out of theatre with immediate effect.
The Trump administration has accused Iran of supporting "imminent attacks" on US personnel in the region and has used a burst of diplomacy and briefings to try to win support for an increasingly aggressive stance against Tehran.
Secretary of State Mike Pompeo told media on May 6 that "it is absolutely the case that we've seen escalatory action from the Iranians", but he also said he couldn't be more explicit. "This threat stream, let me tell you, is real", he added, comparing it to the situation in 2011 in Iraq when US installations were under direct attack.
The White House says that Iran is sowing instability across the region. "Neither we nor them (the US) seek war", he said.
But he noted pointedly that German security agencies and intelligence services do not share the view that the threat of an Iranian military strike is escalating.
Separately, Iran's foreign minister said sanctions imposed by the Trump administration are "unacceptable" but added that his country is committed to an global nuclear deal that has steadily unraveled amid rising tensions.
Shiite-majority Iraq has been under pressure from the U.S. to limit its ties with neighboring Iran, particularly after Washington a year ago withdrew from the 2015 nuclear deal with Tehran and hit it with sanctions.
And in Moscow, President Vladimir Putin's spokesman Dmitry Peskov on Wednesday expressed concerns about "the continued escalation of tensions around this subject".
Some observers speculate that Tehran is seeking to retaliate over Washington's decision in April to put Iran's Revolutionary Guards on a terror blacklist - a move created to stymie their activities across the Middle East.
The Netherlands has suspended its military training mission to northern Iraq, citing an unidentified "risk to security".
Khamenei told Iranian officials the standoff "is not military because there is not going to be any war". The Qatari-owned Al Jazeera network reported May 15 that Foreign Minister Mohammad Bin AbdulRahman Al Thani visited Tehran in recent days aiming to defuse tensions with Washington.
According to a statement by the UK's Ministry of Defense, the decision was made because of "a range of threats to United Kingdom and coalition forces" related to "Iran's destabilizing behavior in the region".
Now that the next wave of a proxy war is mounting, these Iraqi factions might once again rise as an Iranian tool to confront U.S. pressure.