Trump said the USA "reserves the right to defend our personnel, our facilities, our interests, and calls upon all nations to condemn Iran's attempts to disrupt freedom of navigation and global commerce".
The drone was "immediately destroyed", Trump said, after it approached within 1,000 yards (914 meters) of the Boxer, Trump said. "It was threatening the safety of the ship and its crew", said Trump.
A USA defense official said earlier this week that America "has suspicions" that Iran had seized the oil tanker when it turned off its tracker in the Strait of Hormuz.
Tehran downed an American surveillance drone in June, prompting Trump to order air strikes against Iran.
This story is developing and will be updated. In May 2018, Trump pulled the United States out of the agreement, which he called a "disastrous" deal that would not prevent Iran from obtaining a nuclear weapon.
The seizure comes after the Panamanian-flagged tanker MT Riah, which is based in the United Arab Emirates, disappeared from ship tracking maps in Iranian territorial waters on July 14.
The seizure adds another layer of complexity to Iran's standoff with the US - and its insistence that European countries that signed a landmark nuclear deal in 2015 keep their promise to ease economic sanctions, despite the USA withdrawal from the pact.
US Congressional Black Caucus Call For A$AP Rocky's Release
The platinum-selling, Grammy-nominated artist has collaborated with Kendrick Lamar, Cardi B, Drake and Selena Gomez. On Friday, Espaillat, a New York Democrat, said he was pushing to help Rocky come home. "I'm A$AP Rocky.
Trump tweets are latest UK-US flashpoint
In an interview on Fox & Friends on Monday morning , Sen. "But this isn't what our country is about", Trump said. Citizenship and Immigration Services, told CNN on Monday: "I wouldn't go that far, no, certainly not".
Zimbabwe suspended by ICC over government interference
The player will need to be a like-for-like substitute, and any such switch will need to be approved by the Match Referee. Moreover, the punishment for slow over-rate has been changed.
After Trump pulled the United States out of the Iran nuclear deal past year and imposed additional economic sanctions, the Iranians have pushed back on the military front, allegedly sabotaging Saudi and other oil tankers in the Gulf, shooting down a US drone on June 20 and stepping up support for Houthi rebels in Yemen.
Iran has been blamed by the U.S. for attacks on tankers since May in the world's key shipping area.
The statement also says the patrolling units of the IRGC Navy keeps confronting organized smuggling and will defend the interests of the Iranian nation.
Iran's state television station did not identify the vessel.
Tensions between Iran and Britain have been high too, with the United Kingdom seizing an Iranian oil tanker off the coast of Gibraltar.
Citing U.S. defense officials, CNN reported that the Iranian drone was brought down by counter-drone jamming equipment, which was operated by U.S. marines aboard the USS Boxer.
The Guards didn't detail the name or origin of the vessel. They later fell, however, on weakness in USA equities markets and an expectation that crude output would rise in the Gulf of Mexico following last week's hurricane in the region.
Describing Tehran's recent nuclear pronouncements as "unacceptable", German Foreign Minister Heiko Maas said other parties to the deal expected Tehran to uphold its side of the accord.