Germany and the Netherlands have suspended their training of Iraqi soldiers, it emerged on Wednesday.
Israeli Prime Minister Benjamin Netanyahu is urging neighboring countries to support the US against Iran's mounting aggression.
Republicans - and even some Democrats - who have been briefed said the threats are legitimate.
His visit came after Washington announced the deployment of an aircraft-carrier battle group and a bomber task force to the Middle East, which US official said was in response to threats from Iran to the interests of the United States or its allies in the region.
Pompeo, in the meantime, issued a similar comment while on a visit to the Russian city of Sochi on Tuesday, stating that the U.S. "fundamentally doesn't seek a war with Iran".
Last week, the U.S. dispatched warships and bombers to the Middle East to deter what it deemed Iranian threats.
After Ghika's comments drew a sharp retort from the US Central Command, Britain's defense ministry said Wednesday they have "long been clear about our concerns over Iran's destabilising behavior in the region" - while still not confirming any new imminent danger.
In total, the German military has 160 troops on the ground in Iraq, with 60 of them stationed in the Taji Camp training members of the Iraqi army, while the other 100 are based in Erbil and provide military training to Peshmerga forces.
As tensions in the region surge, Foreign Secretary Jeremy Hunt said British officials are anxious about the risk of a conflict between the U.S. and Iran which neither side intends.
"The German army has suspended the training", defence ministry spokesman Jens Flosdorff said, adding there was "generally heightened alert, awareness" for soldiers now operating in the region. "The much more appropriate analogy is Iraq 2011".More news: PG&E lines blamed for deadliest wildfire in California history
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"We will actually with our partners also be deliberate in considering our response, what to do about it, how to deal with it", he said, adding that the United States and France are helping with the probe.
The obvious comparison is with 16 years ago, when President George W. Bush's administration launched its invasion of Iraq.
The US has about 5,000 troops in Iraq and about 2,000 in Syria as part of the coalition campaign to defeat the Islamic State group there. During that, the United States came close to being defeated outright.
Many traditional United States allies are concerned about the threat of yet another conflict in the region.
"They know it will not be in their interest". "They said if the U.S. were attacked on Iraqi soil, it would take action to defend itself without co-ordinating with Baghdad".
Iraq's Prime Minister, Adel Abdul Mahdi, said on Tuesday that its security forces had not observed "movements that constitute a threat to any side". However, the source indicated the United States does not now have evidence that Iranian personnel played any direct operational role.
Iran is exercising "maximum restraint in spite of the fact the United States withdrew from (the) JCPOA last May", Zarif said at the start of his meeting with Japanese Foreign Minister Taro Kono.
Former CIA chief John Brennan responded by tweeting, "Your refusal to accept the unanimous assessment of U.S. Intelligence on Iran, No. Korea, ISIS, Russia, & so much more shows the extent of your intellectual bankruptcy". Large holes were found in the hulls of the tankers, but no evidence has been released showing a link to Iran.
The United States has sent further military forces to the Middle East, including an aircraft carrier, B-52 bombers and Patriot missiles, in a show of force against what U.S. officials say are Iranian threats to its troops and interests in the region.
There were repeated warnings from Washington justifying the military build-up, based on what Mr Pompeo described as an "escalation" in activities by Iran.
He then opined that Iran is in a better position "to strike America on the economic ground" and suggested that "Saudi Arabia and the United Arab Emirates depend on the United States" for their security and at the same time, they are acting as "oil reservoirs" for America.