"It is a major escalation. Ballistic missiles openly launched from Iran onto American targets is a new phase," said Phillip Smyth, an expert on Iran-backed militias.
Trump did not go on evening television to address the nation -- something of an informal presidential tradition in times of foreign policy crises. But he said to expect a statement early Wednesday.
Oil prices immediately jumped on the news, with the benchmark WTI spiking more than 4.5 percent to $65.54 a barrel before receding slightly.
In the US, the aviation regulator banned civil flights over Iraq, Iran and the Gulf, citing the potential for "misidentification" of aircraft.
The slide into open confrontation followed days of sabre rattling between Washington and Tehran, coupled with growing confusion over the future of US troops in Iraq, where many are outraged at the drone strike.
At Soleimani’s funeral in Iran on Tuesday, top Revolutionary Guards commander Major General Hossein Salami vowed "revenge."
Earlier, Trump warned that "if Iran does anything that they shouldn’t be doing, they’re going to be suffering the consequences and very strongly."
He called Soleimani -- for years the mastermind of Iran’s regional network of official and covert military and anti-US alliances -- "a monster."
Trump, however, did walk back earlier threats to bomb Iranian cultural sites in the event of conflict -- something that could be a war crime.
At Soleimani’s funeral in the Iranian city of Kerman, tragedy was added to the geopolitical tensions, when 56 people died and 213 were injured in a stampede as the vast crowd of mourners got out of control, local media reported.
Iran’s Fars news agency reported that the commander was interred on Tuesday night.- Foreign troops waver -
Hours before Iran struck, Trump tried to end confusion over his plans for the approximately US 5,200 troops in Iraq, saying they should stay despite calls by the Iraqi parliament for their expulsion.
"At some point we want to get out, but this isn’t the right point," Trump told reporters at the White House.
Despite Washington’s assurances, several allies started to leave, raising questions over the future of a US-led mission to help the Iraqis fight Daesh.
Canada announced that some of its estimated 500 troops will withdraw to Kuwait and NATO said it also was temporarily "repositioning" some personnel to locations inside and outside Iraq.
Several other countries, including Germany and Romania, announced plans to move forces. France and Italy said they had no intention of withdrawing troops from Iraq.
