President Donald Trump has said Iran appears to be "standing down" and said no Americans were harmed in Iran's ballistic missile strike on two Iraqi bases housing US troops.

Iranian forces fired missiles at military bases housing US troops in Iraq early on Wednesday, saying it was in retaliation for the killing in a US drone strike of powerful Iranian commander Qassem Soleimani on January 3.

But speaking from the White House later in the day, Trump seemed intent on de-escalating the crisis, indicating that he would not retaliate militarily for the strikes.

Instead, he said the US would immediately put in place new economic sanctions "until Iran changes its behaviour" after that country's most brazen direct assault on America since the 1979 seizing of the US Embassy in Tehran.

The president said there were no US citizens harmed in the attack, a fact for which Americans should be "extremely grateful and happy."

Trump, flanked by Vice President Mike Pence, Defence Secretary Mark Esper and Secretary of State Mike Pompeo and military officers, also said he will ask NATO to become "much more involved in Middle East process."

He also used his address to speak directly to Iran, saying "we want you to have a future and a great future," adding the US is ready to "embrace peace and all who seek it".

Donald Trump reacts to Iran’s missile attack_1
Inset: Iranians want to seek revenge against the US over the assassination of its top commander.

-with AAP