The US ship turned back upon receiving a warning to stay away from a damaged Iranian fishing boat, according to the Tasnim news agency.
The Iranian ship then towed the fishing boat, which had sent out a distress signal after taking on water, back to shore.
The agency did not specify when the incident, close to the Strait of Hormuz, took place.
The US Naval Forces Central Command (Navcent) appeared to play down the incident when it denied that any direct contact was made.
It said in a statement the coastal patrol USS Tempest, operating in the Gulf of Oman on 6 September, heard the distress call of an unidentified small boat about 75 nautical miles from its position.
The Iranian motor vessel Nordic Voyager was located much closer to the stricken craft, according to Navcent, and offered help at the same time as the US ship.
The Tempest offered to support the Nordic Voyager but the offer was declined, Navcent said.
Following the radio traffic from a distance, USS Tempest heard the Nordic Voyager coordinate additional Iranian Navy help to tow the vessel in distress back to Iran.
“At no time was there any direct contact between the US and Iranian maritime forces,” Navcent spokeswoman Chloe Morgan said.
Tensions have increased between the Iranian and American military in the Gulf in recent months after Donald Trump warned during the presidential campaign that any Iranian vessels harassing the US Navy would be “shot out of the water”.
In July, a US Navy ship fired warning shots when an Iranian vessel came within 150 yards of it in the Gulf in the first such incident since President Donald Trump took office in January, US officials said.
And in August, an unarmed Iranian drone came within 30 metres of a US Navy warplane as it prepared to land on an aircraft carrier in the Gulf, according to a US official.
Animosity between the two countries has its roots in the 1979 Iranian Revolution, which overthrew the pro-American Shah and replaced him with an Islamist regime.
Tensions eased when President Barack Obama lifted sanctions on Tehran last year as part of a deal to curb its nuclear programme, but Mr Trump announced fresh sanctions in July in response to Iran’s nuclear missile testing.
Serious differences also remain between the two nations in regards to the ongoing conflicts in Syria and Iraq.
The Trump administration is so far maintaining a tough line on Iran and recently warned that while Tehran was complying with the worldwide agreement on nuclear weapons, the country was not following the spirit of the accord and that Washington would look for ways to strengthen it.
Relations between the two nations were also strained when Iran was included in the list of seven nations whose citizens were temporarily halted from entering the US in January under Mr Trump’s controversial “travel ban”.
Within two days of the executive order on the travel ban being signed, Iran conducted a ballistic missile test, which the US government said was a violation of a UN security council resolution.
Reuters contributed to this report