Iraqi counter-terrorism forces stand guard in front of the US embassy in the capital Baghdad on January 2, 2020.

Small rockets hit the area in or around the Green Zone in Iraq's capital of Baghdad late Wednesday, a day after Iran launched missiles at bases housing U.S. and other coalition forces in Iraq, American military officials said.

There was no casualties to U.S. or other coalition forces in the area, and no damage to facilities in the Green Zone, which contains the American embassy and other Western diplomatic posts, officials said.

The Dow Jones Industrial Average pared gains following initial reports Wednesday of an explosion in Baghdad just before midnight local time. It closed 161 points higher but about 80 points lower than it had been just before the news.

Iraq's military said two Katyusha rockets fell inside the Green Zone.

There were no casualties, according to the statement from Iraq's military.

A coalition spokesman later confirmed the attack.

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The rockets were fired several hours after President Donald Trump declared that Iran appeared to be standing down from military conflict with the U.S. — remarks that sent stock indexes surging higher.

On Tuesday night Eastern time, Iran launched missile attacks against two Iraqi bases that house U.S. military and coalition forces.

The barrage was retaliation for the killing on Thursday of Iran's top military leader, Gen. Qasem Soleimani, in a U.S. airstrike in Baghdad.

Trump on Wednesday defended the decision to target Soleimani, who has been blamed for the deaths of hundreds of Americans in the Middle East.