The tanker and four behind it were finishing a high seas journey amid a burgeoning relationship between Iran and Venezuela.
Venezuela’s defense minister said the armed forces will escort Iranian tankers arriving with fuel to the country.
The Navy will take “lawful defensive measures” against vessels in the Mideast that come within 100 meters of its warships.
All the vessels involved belong to Iranian state-owned or state-linked companies, flying under the Iranian flag.
Authorities said the Konarak was too close to a target and was accidentally hit in an incident that also wounded 15 troops.
Iranian media said the Konarak had been overhauled in 2018 and was able to launch sea and anti-ship missiles.
He said the amphibious assault ship Boxer took defensive action after the drone closed to within 1,000 yards of the warship.
Trump administration officials said they consider the release of American hostages and detainees to be a high priority.
Tensions rose after the Trump administration withdrew from the nuclear deal between Tehran and world powers in 2018.
U.S. officials believe they’re making progress in efforts to secure the release from Iran of a detained Navy veteran.