Washington ordered the evacuation of non-emergency staff from its Baghdad embassy last month due to an alleged growing threat from Iranian-linked Iraqi militias, while Germany and the Netherlands suspended their training missions.

But Canadian General Dany Fortin, who leads NATO's 500-strong training and advisory mission in Iraq, said his forces had "sufficiently mitigated" the threat and were able to continue working.

"There's no doubt there's still risk and as reported in the media in the last few weeks there was a critical threat, cause for concern for the US and for all of us," Fortin told reporters at NATO headquarters in Brussels.

"We have force protection measures in place to ensure that we're vigilant, unpredictable, we change things, but we can continue our activities. So it hasn't affected our advising, our training activities whatsoever."

The NATO mission aims to train local Iraqi forces and improve military education centres to try to avoid a repeat of 2014, when the so-called Islamic State group seized large areas of Iraq and Syria.

Fortin said the aim was to create a "self-sustainable" system of forces and training in Iraq, adding that he hoped this could be achieved in three to four years.

The US evacuation order last month came after the Pentagon deployed a carrier task force and B-52 bombers to the Gulf to deter an unspecified threat from Tehran to US forces or allies.

Despite international scepticism, the US government has been pointing to increasing threats from Iran, a long-time enemy and rival of US allies Israel and Saudi Arabia.

Washington has also decided to deploy an extra 1,500 troops to the region, while stepping up economic sanctions against Tehran.

The swingeing economic penalties came after the US pulled out of the 2015 Iran nuclear deal, imperilling an accord that many of Washington's allies say is the best way to stop Tehran developing atomic weapons.