Iran shot down a U.S. surveillance drone Thursday in the first direct military contact between the two nations in more than 30 years. But where it happened is in dispute. Iran said it was over their territory, while the U.S. said the plane was over international waters.

The drone left a corkscrew smoke trail as it fell tens of thousands of feet into the sea after being hit by an Iranian missile, a direct attack by Iran on a U.S. military aircraft.

"Iran made a big mistake. This drone was in international waters clearly. We have it all documented, it's documented scientifically, not just words, and they made a very bad mistake," President Trump said.

When asked how he will respond, Mr. Trump responded, "You'll find out." But after that, the president seemed to give Iran's leaders the benefit of the doubt.

"I have a feeling — I may be wrong and I may be right, but i'm right a lot — I have a feeling that it was a mistake made by somebody that shouldn't have been doing what they did," he said.

Mr. Trump pointed out there was no loss of life since the drone was unmanned and laid the destruction of a $110 million aircraft off on some trigger happy officer down in the ranks.

"I think it could have been someone who was loose and stupid that did it," he said.

The shoot down of the Global Hawk occurred just after 4 a.m. local time. A map released by the Pentagon showed the location of the Iranian missile battery and the drone, which the U.S. military said was more than 20 miles off the coast of Iran at the time. It's the same area where last week two tankers were attacked by what the U.S. said were Iranian mines.

Iran's foreign minister tweeted coordinates that put the shoot down closer to Iran and claimed "we've retrieved sections of the U.S. military drone in our territorial waters."

Iran has now taken two shots at U.S. drones in the past seven days. It missed the first time and hit the second. If the president wanted to, that's enough to justify a military strike against Iranian anti-aircraft sites.

In a letter to the U.N., Iranian ambassador Majid Takht Ravanchi said his country has the right to "vigorously defend its land, sea and air."

"While the Islamic Republic of Iran does not seek war, it reserves its inherent right, under Article 51 of the United Nations Charter, to take all appropriate necessary measures against any hostile act violating its territory, and is determined to vigorously defend its land, sea and air," Ravanchi wrote.

He said the incident wasn't the first time the U.S. conducted a "provocative act" against Iran's "territorial integrity."

"The international community is called upon to demand the United States to put an end to its continued unlawful and destabilizing measures in the already volatile region of the Persian Gulf," Ravanchi added.

Pam Falk contributed to this report.