Washington — President Trump said no Americans or Iraqis were hurt in an Iranian missile attack on two military bases housing U.S. troops in Iraq, and said Iran "appears to be standing down" in the explosive confrontation between the U.S. and the Islamic Republic.

"I'm pleased to inform you, the American people should be extremely grateful and happy. No Americans were harmed in last night's attack by the Iranian regime," the president said in an address to the nation from the White House on Wednesday. "We suffered no casualties, all of our soldiers are safe and only minimal damage was sustained at our military bases."

Flanked by the vice president, defense secretary, secretary of state and military leaders in the grand foyer of the White House, Mr. Trump announced the U.S. will "immediately impose additional punishing economic sanctions" against Iran. He also said he would ask NATO allies to become "much more involved" in the Middle East.

President Trump addresses the nation from the White House on Wednesday, January 8, 2020. Evan Vucci / AP

"Iran must abandon its nuclear ambitions and end its support for terrorism," Mr. Trump declared, calling on European allies to scrap the 2015 nuclear deal with Iran.

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The president's address came hours after Iran fired at least a dozen ballistic missiles at the Al Asad and Erbil bases in Iraq, where U.S. and coalition personnel are stationed. The strikes came in retaliation for the U.S. strike on Friday that killed Iranian Major General Qassem Soleimani, the country's most prominent military leader and head of Iran's elite Quds Force.

Mr. Trump called Soleimani a "ruthless terrorist" whose hands "were drenched in both American and Iranian blood." He added that Soleimani "should have been terminated long ago."

The Soleimani strike set off a wave of outrage in Iran, prompting millions of people to take to the streets across Iran amid vows of revenge by the Iranian leadership. Supreme Leader Ali Khamenei called Wednesday's missile strike "slapped [the Americans] in the face," saying Iran's real revenge will be forcing the U.S. to pull out of the region.

But the lack of casualties and minimal damage from the missile strikes prompted speculation that the attack might lead to a de-escalation of tensions, allowing Iran to save face domestically by exacting a relatively minor degree of revenge for Soleimani's killing. Mr. Trump first hinted at this dynamic in a tweet following the strikes.

"All is well! Missiles launched from Iran at two military bases located in Iraq. Assessment of casualties & damages taking place now. So far, so good! We have the most powerful and well equipped military anywhere in the world, by far! I will be making a statement tomorrow morning," the president tweeted.

Mr. Trump concluded his remarks Wednesday by directly addressing the Iranian people.

"We want you to have a future, and a great future, one that you deserve," Mr. Trump said. "The United States is ready to embrace peace with all who seek it."

Tune in to CBSN on Wednesday at 8 p.m. ET to watch "Crisis in the Middle East: Fears of War."