State media initially said the servicemen were killed in a "misguided missile attack," but later made references to the nature of the incident, warning people not to "speculate" about it.
The incident happened near the southern Iranian port city of Jask. Iranian authorities later released images of the Konorak ship docked at a port in an apparent attempt to remove rumors that the vessel had sunk.
Konorak, a logistic vessel armed with a 20 mm caliber cannon and cruise missile shooters against ships, was injured at night, according to official and semi-official media. Konorak also goes on reconnaissance missions and lays mines. About 40 people were on board.
Iran, already under strain from US sanctions, is also tackling one of the world's largest outbreaks of the coronavirus pandemic.
The tweet came after the US Navy posted a video saying it said Iranian naval vessels repeatedly "took dangerous and harassing approaches" to US Navy warships in the North Arabian Sea. The naval defense claimed that one Iranian vessel arrived within 10 meters of a US ship collision.