Shortly before, Trump had tweeted that "Iran made a very big mistake" after a top Iranian commander warned Iran was "ready for war."
When asked early afternoon whether the U.S. would strike back during an Oval Office meeting with Canadian Prime Minister Justin Trudeau, Trump said: "You'll soon find out."
But at the same time, he said, "I find it hard to believe it was intentional if you want to know the truth."
"It could have been somebody who was loose and stupid that did it," he said.
"I would imagine it was a general or somebody who made a mistake in shooting the drone down," Trump said. "Fortunately, that drone was unarmed. It was not -- there was no man in it, it was in international waters but we didn't have a man or woman in the drone, we had nobody in the drone. Would have made a big, big difference."
"I have a feeling -- and I may be wrong and I may be right but I'm right a lot -- that it was a mistake made by somebody that shouldn't have been doing what they do," he said. "I think they made a mistake and I'm not just talking about the country made a mistake somebody under the command of the country made a mistake."
"It was a very foolish move," he said. Nevertheless, he said, "This country will not stand for it."
Iran continued to maintain that the American drone indeed violated its airspace and made no mention of Trump's suggestion the shootdown was a mistake.
Congressional leaders were invited to an afternoon briefing in the White House Situation Room, at which Trump presided.
Afterward, at the Capitol, Senate Minority Leader Chuck Schumer of New York told reporters, "The president may not intend to go to war here, but we're worried that he and the administration may bumble into a war. We told the room that the Democratic position is that congressional approval must be required before funding any conflict in Iran."
Earlier, the president did not respond when ABC News asked him for a comment as he walked into the West Wing late Thursday morning. A White House official confirmed he was headed into a meeting with Acting Defense Secretary Patrick Shanahan and Secretary of State Mike Pompeo.
Top congressional leaders were invited to an afternoon briefing in the White House Situation Room, a source said. Trump was expected to attend.
A U.S. official confirmed to ABC News that the U.S. Navy was working to recover the drone in a debris field the official said was located in international waters near the Strait of Hormuz. At a short, mid-day Pentagon briefing, a U.S. military official speaking from the region reiterated that the drone was shot down in international airspace.
The commander of U.S. Air Forces Central Command, Lt. Gen. Joseph Guastella, said the American drone was flying over the Gulf of Oman near the Strait of Hormuz on a surveillance mission near previous tanker attacks when it was shot down by a surface-to-air missile fired from a location in the vicinity of Goruk, Iran.
The Pentagon released a grainy video it said showed the shootdown and a plume of smoke.
Calling the strike an "unprovoked attack," Guastella said it was "an attempt to disrupt our ability to monitor the area following recent threats to international shipping and free flow of commerce." He said the drone was operating "at high-altitude approximately 34 kilometers from the nearest point of land on the Iranian coast" when it was shot down, falling into international waters.
The incident was sure to trigger serious discussions within the Trump administration about how to respond to a direct attack on a U.S. military asset that goes beyond recent attacks in the Middle East that the U.S. has blamed on Iran.
Mid-morning Thursday, White House press secretary Sarah Sanders said that President Trump has "been kept up to date" and was briefed both Thursday morning and Wednesday night. She said the White House would “keep in touch with members on the Hill.”
Top congressional leaders from both parties and chairs and ranking members of the Intelligence, Foreign Affairs and Armed Services Committees received a closed-door classified intelligence briefing from Trump administration officials at the Capitol.
House Speaker Nancy Pelosi told reporters that at least 20 of the top lawmakers on Capitol Hill were invited to attend the exclusive briefing.
“I think it's a dangerous situation,” Pelosi said. “We have to be strong and strategic about how we protect our interests. We also cannot be reckless in what we do. So, it would be interesting to see what they have to say, whether the - I don't think the President wants to go to war. there's no appetite for going to war in our country.”
A close ally of the president, Sen. Lindsey Graham, R-S.C., when asked how the U.S. should respond, answered, "With firmness, and resolve. The only way Iran changes its behavior is that if they believe Americans will put options on the table that will create pain for the regime."
Graham said he had spoken with the president.
"I talked to him last night. He had a meeting last night. He believes that we're going into a we're getting into a bad space, that his options are running out, that he's not going to be intimidated to redo a nuclear deal. That was terrible. He's not going to relieve sanctions because the Iranians are worse than they been. The Iranian deal was to get them to change their behavior, the nuclear deal. They did everything but change their behavior," Graham told reporters.
"I think what President Trump believes is that this regime is spoiling for a fight but they understand how a conflict would end, it would end badly for them. He does want to try and get a better deal but not this way," he said.
There was a National Security Council meeting at the White House earlier Thursday morning to discuss Iran, an administration official said, which Shanahan and Joint Chiefs Chairman Gen. Joseph Dunford attended. Another NSC meeting was to take place Thursday afternoon, which U.S. officials said Vice Chairman of the Joint Chiefs of Staff Gen. Paul Selva and Pompeo would attend, officials said.
Gen. Hossein Salami, commander of Iran's Islamic Revolutionary Guard Corps, offered a strongly worded threat to the U.S. after the drone was downed.
"Shooting down the American spy drone had a clear, decisive, firm and accurate message," he said, translated from Farsi. "The message is that the guardians of the borders of Islamic Iran will decisively respond to the violation of any stranger to this land. The only solution for the enemies is to respect the territorial integrity and national interests of Iran."
"We do not intend to engage in war with any country, but we are completely ready for the war. Today’s incident is a clear sign of this accurate message," Salami added.
Earlier, Iranian state media had quoted Iran's Islamic Revolutionary Guard Corps as saying it had downed the drone when it entered Iranian airspace near the Kouhmobarak district north of the Strait of Hormuz.
Iran's foreign minister, Javad Zarif, tweeted, "The US wages #EconomicTerrorism on Iran, has conducted covert action against us & now encroaches on our territory. We don't seek war, but will zealously defend our skies, land & waters. We'll take this new aggression to #UN & show that the US is lying about international waters."
After Trump spoke, Zarif tweeted specific information about Iran's claims.
"Iranian reports that the aircraft was over Iran are false," said CENTCOM spokesperson Navy Capt. Bill Urban in a statement on Thursday morning, before Zarif's most recent tweet. "This was an unprovoked attack on a U.S. surveillance asset in international airspace."
Urban said the RQ-4A Global Hawk, which "provides real-time intelligence, surveillance and reconnaissance missions (ISR) over vast ocean and coastal regions," was shot down by an Iranian surface-to-air missile system while operating in international airspace over the Strait of Hormuz at approximately 11:35 p.m. GMT on June 19.
The incident is not the first time in recent days that Iran has targeted an American drone off its coast.
Last Thursday, Iran attempted to shoot down an MQ-9 Reaper that was surveilling the attack on one of two tankers in the Gulf of Oman. The United States has blamed Iran for being responsible for the attacks on the two tankers -- a claim Iran has denied.
"According to our assessment, a modified Iranian SA-7 surface-to-air missile attempted to shoot down a U.S. MQ-9, at 6:45 a.m. local time, June 13, over the Gulf of Oman, to disrupt surveillance of the IRGC attack on the M/T Kokuka Courageous," CENTCOM spokesperson Lt. Col. Earl Brown said in a statement to ABC News on Saturday.
"Subsequent analysis indicates that this was a likely attempt to shoot down or otherwise disrupt the MQ-9 surveillance of the IRGC attack on the M/T Kokuka Courageous," Brown said.
In early May, the Pentagon rushed the aircraft carrier USS Abraham Lincoln and a B-52 bomber task force to the Middle East to deter possible attacks by Iran or Iranian-backed groups on U.S. forces and U.S. interests in the region.
ABC News' Somaye Malekian, John Parkinson and Mariam Khan contributed to this report.