Earlier, Trump said the US is targeting 52 sites in Iran and will hit them "very fast and very hard" if the Islamic republic attacks American personnel or assets.
In a sabre-rattling tweet that defended Friday's US drone strike assassination of a powerful Iranian general in Iraq, Trump said 52 represents the number of Americans held hostage at the US embassy in Tehran for more than a year starting in late 1979.
Trump said some of these sites are "at a very high level & important to Iran & the Iranian culture, and those targets, and Iran itself, WILL BE HIT VERY FAST AND VERY HARD. The USA wants no more threats!"
Trump spoke out after pro-Iran factions ramped up pressure on US installations across Iraq with missiles and warnings to Iraqi troops — part of an outburst of fury over the killing of Qasem Soleimani, described as the second most-powerful man in Iran.
With the Islamic republic promising revenge, his killing was the most dramatic escalation yet in spiraling tensions between Washington and Tehran and has prompted fears of a major conflagration in the Middle East.
In the first hints of a possible retaliatory response, two mortar rounds hit an area near the US embassy in Baghdad on Saturday, security sources told AFP. Almost simultaneously, two rockets slammed into the Al-Balad airbase where American troops are deployed north of Baghdad, security sources said.
The Iraqi military confirmed the missile attacks in Baghdad and on al-Balad and said there were no casualties. The US military also said no coalition troops were hurt.
With Americans wondering fearfully if, how and where Iran will hit back for the assassination, the US Department of Homeland Security issued a bulletin that said "at this time there is no specific, credible threat against the homeland."
However on Saturday the website of the Federal Depository Library Program, a little-known US government agency, was breached by a group claiming to be linked to Iran, who posted graphics displaying the Iranian flag and vowing revenge for Soleimani's death.
Separately, US Speaker of the House Nancy Pelosi said in a statement that information given to Congress by Trump, a Republican, "prompts serious and urgent questions about the timing, manner and justification of" the strike.
"The Trump Administration's provocative, escalatory and disproportionate military engagement continues to put service members, diplomats and citizens of America and our allies in danger," said Pelosi, a Democrat.
Another prominent democrat, Alexandria Ocasio-Cortez, called the president a "monster", for "threatening to target and kill innocent families, women and children". In a tweet, she said: "This is a war crime."