The US military is tracking the ship after Tehran reportedly said it would send warships to escort the vessel to Yemen, Pentagon spokesman Colonel Steven Warren told reporters.
The ship, the Iran Shahed, had moved through the Strait of Hormuz and was now in the Gulf of Oman, according to the marinetraffic.com site. But the vessel was not under any naval escort at the moment, Warren said.
"We are monitoring the Iranian ship," he said. "We are aware of the Iranians' statement that they plan to escort this ship with warships."
The state Iranian IRNA news agency earlier quoted a naval commander, Rear Admiral Hossein Azad, saying naval forces would be "safeguarding" the vessel.
Iran's Red Crescent had said last week that it would send a ship carrying 2,500 tons of humanitarian aid to Yemen, where Tehran-backed Huthi rebels are fighting pro-government forces supported by a Saudi-led coalition.
"The Iranians have stated that this is humanitarian aid," Warren said.
"If that is the case, then we certainly encourage the Iranians to deliver that humanitarian aid to the United Nations humanitarian aid distribution hub, which has been established in Djibouti."
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"This will allow the aid to be rapidly and efficiently distributed to those in Yemen who require it," he added.
When asked if the US military would try to search the ship or prevent it from docking in Yemen, Warren declined to comment.
State Department spokesman Jeff Rathke confirmed the United States was "certainly tracking this convoy closely."
"We would discourage any provocative actions," he added.
The warnings from Washington raised the possibility of a potential confrontation at sea after tensions flared in recent days in the Strait of Hormuz.
The US Navy bolstered its presence in the Gulf after Iran seized a Marshall Islands-flagged vessel in the vital waterway.
Iranian authorities later released the ship, citing a commercial dispute with Denmark's Maersk group, which chartered the vessel.
"If the Iranians are planning some sort of stunt in the region, they know as well as we do that it would be unhelpful and in fact could potentially threaten the ceasefire (in Yemen) that has been so painstakingly brought about," Warren said.
"We call on the Iranians to do the right thing here and deliver their humanitarian aid in accordance with UN protocols which is through the distribution hub that's been established in Djibouti," he added.