Trump told reporters: "Iran made a big mistake. This drone was in international waters, clearly. We have it all documented scientifically not just words. And they made a very bad mistake".
Asked how the US would respond, Trump said: "You'll find out".
At the same time, reflecting his reluctance for a war, Trump left room for a compromise hinting that the Iranian leadership was not behind it. "I imagine someone made a mistake," he said and added that he thought it was someone "loose and stupid who did it."
Trump has said in the past that he does not want to go to war with Iran. He has generally opposed US military entanglements abroad and has sought to get out of Afghanistan and Syria.
Contradicting Trump, Tehran asserted that the drone was in Iranian territory when it was brought down.
The Islamic Revolutionary Guards Corps (IRGC) said the US "RQ-4 Global Hawk" was brought down by its Air Force near the Kouh-e Mobarak region, which sits in the central district of Jask county, after the unmanned plane violated Iranian airspace.
IRGC chief said: "The downing of the American drone was a clear message to America... Our borders are our red line and we will react strongly against any aggression". But he also said that Iran did not want a war.
The escalation comes in the wake of the attacks on two oil tankers in the Strait of Hormuz last week that the US said was carried out by Iran. Tehran, however, has denied it.
Trump, who opposes foreign military action, faces strong pressures from some in his administration and his party to attack Iran.
"If they're itching for a fight, they'll get one", Republican Senator Lindsay Graham said.
He warned: "Iran needs to get ready for severe pain inside their country. Their capability pales in comparison to ours. We won't let them disrupt navigation of the seas, attack our allies and US interests without paying a price".
Another Republican Senator, Tom Cotton, in an interview to Politico, called for bombing Iran.
Trump's National Security Adviser John Bolton has been advocating a strong action against Iran. Earlier this week, Secretary of State Mike Pompeo reportedly told members of US Congress that Iran was linked to al-Qaeda creating a possible justification for war.
Iran has the capability to shut down the strait of Hormuz, through which 20 percent of global oil production moves.
Democrat Speaker Nancy Pelosi said: "I don't think the president wants to go to war. There's no appetite to go to war in our country."
While acknowledging that "high tension wires are up in the region" and the US has to be strong protect its interests, she said, "We started to lose credibility on the subject when we walked away from the Iran nuclear agreement."
The current tensions began after Trump renounced the multinational agreement with Iran to stop nuclear proliferation. That pact was signed during his predecessor Barack Obama's administration along with the other permanent members of the United Nations Security Council and Germany.
Trump imposed sanctions on Iran and on trade with it by others, affecting India's oil purchases.
He has offered to hold talks with Iran, which has turned down the initiative.
On Monday Iran said that it had increased production of low-grade uranium and would exceed the limits set by the multi-party nuclear agreement that Trump has renounced.
UN Secretary-General Antonio Guterres said that "the world cannot afford a major confrontation in the Gulf region".
His Spokesperson Stephane Dujarric said: "He appeals to all sides to exercise maximum restraint and avoid any action that can escalate the already tense situation".
(Arul Louis can be reached at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )