A senior Democratic senator demanded President Donald Trump's administration brief Congress on the Iran threat, warning that the US legislature has not approved military action against Tehran.

And Moscow expressed concerns that both Washington and Tehran were dangerously stoking tensions, as the Pentagon ramped up its forces in the Gulf with B-52 bombers, Patriot missiles and an aircraft carrier task force.

The embassy evacuation came 10 days after Trump's national security advisor John Bolton announced the military deployment in response to intelligence on an unspecified "imminent" plot by Iran to attack US forces or allies.

The State Department warned Wednesday of numerous "terrorist and insurgent groups" active in the country, including "anti-US sectarian militias" who could "threaten US citizens and Western companies throughout Iraq."

The warning did not mention Iran specifically, but "anti-US sectarian militias" points to Iran-backed groups.

A State Department spokesman told AFP the departure of non-emergency personnel came in response to "the increased threat stream we are seeing in Iraq."

- Possible attacks -

Washington says it has received intelligence on possible attacks by Iranian or Iranian-backed forces, possibly targeting US bases in Iraq or Syria.

Some observers speculate that Tehran is seeking to retaliate to Washington's decision in April to designate the Islamic Revolutionary Guard Corps of Iran as a terrorist organization in an effort to stymie their activities across the Middle East.

But since the first US warning on May 5, the only activity seen has been a still-mysterious "attack" Monday on four tankers anchored off Fujairah, a UAE port at the strategically crucial entrance to the Gulf.

One or more vessels incurred light hull damage, but what caused the damage and who was behind it remains unknown.

US allies in Iraq have refrained from echoing Washington's warning cry.

Major General Chris Ghika, a British spokesman for Operation Inherent Resolve, the coalition fighting the Islamic State group, said Tuesday there was no special heightened alert, and that OIR troops were always on guard against possible attacks.

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.

Germany and the Netherlands said Wednesday they were suspending training of soldiers in Iraq; German defence ministry spokesman Jens Flosdorff said there was "generally heightened alert, awareness" among soldiers in the region, but gave no specifics.

Separately, the Netherlands' defense ministry said it was suspending a training mission in Iraq due to "threats," according to the Dutch ANP news agency.

- US, Iran both deny war plans -

Both Washington and Tehran said Tuesday they were not seeking war.

"This face-off is not military because there is not going to be any war. Neither we nor them (the US) seek war," Ayatollah Ali Khamenei said Tuesday.

"We fundamentally do not seek a war with Iran," echoed US Secretary of State Mike Pompeo in Sochi, Russia.

But Russia, a major backer of Tehran, expressed concern Wednesday that Pompeo's assurances had not quelled the crisis.

"So far we notice the continued escalation of tensions around this subject," Kremlin spokesman Dmitry Peskov said, a day after Pompeo met with President Vladimir Putin.

Peskov said Washington had provoked Iran, but added that "we are saddened to see the decisions taken by the Iranian side."

In the US Congress Democrats demanded to know why the Trump administration was boosting its forces in the Gulf and, according to media reports, considering military plans including the possibility of sending 120,000 US troops to the Middle East if Iran attacks American assets.

"The Trump administration has not provided any information to this committee on the intelligence behind their decisions, or what they plan to do in Iraq or Iran," said Senator Bob Menendez, the senior Democrat on the Senate Foreign Relations panel.

He demanded a briefing "immediately" on the threat intelligence, any plans for war and the decision to order embassy staff out of Iraq.

"Congress has not authorized war with Iran... If (the administration) were contemplating military action with Iran, it must come to Congress to seek approval," he said.