The US warships were being monitored and tracked by the Zolfaqar flotilla's corvettes, the statement noted, saying the incident occurred only a few days after another American warship had fired shots into the air to warn an IRGC patrol vessel in the Persian Gulf.
United States aircraft carrier Nimitz and an accompanying warship approached Iranian military vessels on Friday at 4 p.m. local time (11:30 GMT) dispatching a helicopter, which flew near the vessels, the statement read.
In a provocative and unprofessional action, the Americans even fired warning shots at the Zulfaqar navy boats; however, the IRGC forces pursued their mission in the region until the USS Nimitz and the other warship left the region in central Persian Gulf.
Iran said the incident took place near one of its oil and gas fields in the Persian Gulf.
This incident followed further confrontation in the Gulf when a USA naval vessel fired warning shots at a Guards vessel as it closed in on the American boat, US officials said Tuesday.
Iranian forces view the American presence in the Gulf as provocative.
Mr Trump in the past has blasted the Iran nuclear accord as "the stupidest deal of all time", but has certified to Congress that Iran is still complying with the terms of the agreement.
In response, Navy spokesman Lieutenant Ian M. McConnaughey called the move "safe and professional".
Mr Araghchi said the new sanctions are "a breach of the deal in articles 26, 28 and 29".
A U.S. official, speaking on the condition of anonymity, said the Iranian boat was armed but its weapons were unmanned.
Iran pledged to forge ahead with its missile program Saturday.
On Friday, the United States, France, Germany and Britain - who brokered the 2015 nuclear deal with Iran along with China, Russia and the European Union - said they're raising concerns with the United Nations over Iran's Thursday launch of a satellite-carrying rocket into space.