US Navy personnel showed reporters pieces of debris and a magnet the Navy said was used to attach an unexploded mine to the Japanese-owned Kokuka Courageous oil tanker, which was attacked on June 13, along with the Norwegian-owned Front Altair tanker.
He also made it clear that Iran is not seeking war with any country but is fully prepared for any confrontation.
In addition, USA officials have said intelligence over the past month and a half has pointed to numerous "threat streams" coming out of the Middle East that "link back to the Iranian regime".
Tehran and Washington have been foes for decades but Trump's arrival in the White House, alongside veteran Mideast hawks like his national security adviser John Bolton, has seen a sharp deterioration in relations. Al Udeid hosts nearly 10,000 United States troops and the USA sent B-52 bombers there last month following threats from Iran.
Russian President Vladimir Putin said any use of force by the United States against Iran "would be a disaster for the region".
Guastella said the drone, a Navy variant of a high-flying Global Hawk, was over the Strait when it was hit and it fell into worldwide waters.
Trump has repeatedly said he does not favor war with Iran unless it is to stop the country getting a nuclear weapon - something Iranian leaders insist they are not pursuing. But a US official said the unmanned aircraft was brought down in worldwide airspace over the Strait of Hormuz.
The US military's Central Command later confirmed that a US Navy Broad Area Maritime Surveillance (BAMS-D) aircraft was shot down by an Iranian surface-to-air missile system while operating in what it said was global airspace over the Strait of Hormuz at approximately 4.05am Iran time on Thursday (11.35am NZT).
"Borders are our red line", Revolutionary Guard commander Gen. Hossein Salami told a crowd in the western city of Sanandaj, in a televised address. Last week, the Trump administration accused Iran of being behind attacks on two oil tankers in the Strait of Hormuz that leads to the Persian Gulf. This is the latest, and most significant, of a series of attacks in the region that have inflamed tensions between Tehran and Washington.
Previously, the US military alleged that Iran had fired a missile at another drone last week that was responding to the attack on two oil tankers near the Gulf of Oman.
In recent weeks, the USA has sped an aircraft carrier to the Mideast and deployed additional troops alongside the tens of thousands already in the region. But we can't let Iran go on a rampage like this.
Mr Trump said it was "documented" that the unmanned drone had been over global waters and not in Iranian airspace. Iran has denied the charge. AFP has reported that Mr Bolton is traveling to Israel to discuss the current escalation.
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