A US Central Command spokesman said a US drone had been observing the Front Altair tanker as it was on fire.
Several minutes later, Iranian Revolutionary Guard troops fired a modified Iranian SA-7 surface-to-air missile to try to bring down the drone in a likely attempt to disrupt the drone's surveillance of the other ship, the Kokuka Courageous, lieutenant colonel Earl Brown said.
Crew members from the Norwegian-owned Front Altair landed in Dubai on Saturday after two days in Iran.
The other tanker targeted in the assault limped into anchorage off the eastern coast of the United Arab Emirates.
Both the mariners' recollection and the physical evidence remaining on the Front Altair and the Kokuka Courageous, now off the coast of Fujairah, will play an important role in determining who the international community blames for Thursday's explosions on board the oil tankers.
Already, the US has blamed Iran for what it described as an attack with limpet mines on the two tankers, pointing to black-and-white footage it captured that American officials describe as Iranian Revolutionary Guard troops removing an unexploded mine from the Kokuka Courageous.
The implication is that Iran wanted to remove any evidence that could link them to the attack. Weapons experts can examine a mine for clues about its manufacturer.
Tehran rejected the allegation, instead accusing the US under president Donald Trump of pursuing an "Iranophobic" campaign against it.
However, Iran previously used mines against oil tankers in 1987 and 1988 in the "Tanker War," which saw the US Navy escort ships through the region - something American officials may consider doing again.
In a new allegation on Saturday, the US military accused Iranian Revolutionary Guard troops of trying but failing to shoot down a US drone to disrupt surveillance of the tankers during the attacks.
All this comes after four other oil tankers off Fujairah suffered similar attacks in recent weeks, and Iranian-allied rebels from Yemen have struck US ally Saudi Arabia with drones and missiles.
Last year Mr Trump withdrew America from the 2015 nuclear deal that Iran reached with world powers and recently imposed a series of sanctions now squeezing its beleaguered economy and cutting deeply into its oil exports.
While Iran maintains it has nothing to do with the recent attacks, its leaders repeatedly have threatened to close the vital Strait of Hormuz, through which 20 per cent of the world's oil flows.
Meanwhile, Britain's ambassador to Iran sought an urgent meeting with the country's Foreign Ministry after the UK broadly backed the US in blaming Tehran for the attacks.
Rob Macaire said his request was granted and rejected reports that he was ordered by Iranian officials to explain Britain's position.
Foreign Secretary Jeremy Hunt said the UK's own assessment of Thursday's events in the Gulf of Oman led British officials to conclude that responsibility for the attacks "almost certainly lies with Iran".
However, Labour leader Jeremy Corbyn said Britain should not act without "credible evidence" Iran was behind attacks on the two oil tankers, which dramatically heightened tensions in the region.