The number of US troops injured by an Iranian missile strike in Iraq this month has risen to 64, according to new figures released by the Pentagon.

US President Donald Trump had initially said no Americans were hurt by the missiles fired on a base housing US soldiers in the country's west on January 8.

Democrats later accused Trump of trying to downplay the injuries.

The American personnel have been diagnosed with mild traumatic brain injury (TBI), Lieutenant Colonel Thomas Campbell, a Pentagon spokesman, said in a statement Thursday.

The Pentagon said Wednesday that 50 soldiers were injured in the Iranian strike on the Ain al-Asad base. The latest total is an increase of 14 on those numbers.

Iran fired on Iraqi bases housing US troops in retaliation for an American drone attack that killed Iranian commander Qasem Soleimani in Baghdad, raising fears of war.

Of those diagnosed with TBI, 39 troops have returned to duty, the Pentagon said, while the rest have either been sent back to the US, are waiting to be sent back or are currently being evaluated.

At the time of the strikes most of the 1,500 American soldiers at the Ain al-Asad base were in bunkers, after they were given advance warning from superiors.