Tehran fired ballistic missiles at two bases in Iraq overnight in the first act of the Islamic republic's promised revenge for the US killing of Qasem Soleimani in Baghdad on Friday, drawing criticism from Western powers.

"I condemn the Iranian missile attacks on US and coalition forces in Iraq. NATO calls on Iran to refrain from further violence," Stoltenberg tweeted.

"Allies continue to consult & remain committed to our training mission in Iraq."

A NATO official said that there were no casualties among the troops on its training mission in Iraq, though on Tuesday the alliance said it was moving some personnel out because of the increased danger following Soleimani's killing.

The 500-strong NATO mission has suspended training activities due to the increased security risks, but Stoltenberg has said it will resume when the situation improves.

US and allied foreign troops in Iraq are concerned they might be targeted by Iran or allied Iraqi militias after the killing of Revolutionary Guards general Soleimani, and some countries involved in the NATO mission have moved their troops out of the country.