Tehran and Washington have traded barbs over a spate of incidents in the past year involving their forces in the sensitive waters of the Gulf.

Their latest high-seas confrontation came on April 15, when the United States said 11 Iranian boats harassed its navy ships in what it described as the international waters of the "Arabian Gulf".

President Donald Trump then tweeted that he had ordered the US Navy to "shoot down and destroy any and all Iranian gunboats if they harass our ships at sea".

Iran's president on Wednesday replied that "the Americans should know that this gulf is called the Persian Gulf, not the New York Gulf or the Washington Gulf".

"They must understand the situation by that name and by the coastal nation that has protected this waterway for thousands of years," Rouhani said in a televised address during a cabinet meeting.

"They should not plot against the Iranian nation every day.

"The soldiers of our armed forces in the guardians of the Revolution, the army, Basij (paramilitary organisation) and the police have always been and will be the guardians of the Persian Gulf."

Iran and the United States have been at loggerheads for decades.

Tensions between them have escalated since 2018 when Trump unilaterally withdrew the US from a multinational accord that froze Iran's nuclear programme and reimposed crippling sanctions on its economy.

The arch enemies have appeared to come close to a direct military confrontation twice since June last year, when Iran shot down a US drone in the Gulf.

On that occasion, Trump cancelled retaliatory air strikes at the last minute.

Trump also opted not to take any military action in January after Iran fired a barrage of missiles at US troops stationed in Iraq.

Iran launched the missiles after a US drone strike near Baghdad airport killed Qasem Soleimani, the general who headed the Revolutionary Guards' foreign operations arm, the Quds Force.