US President, Donald Trump has threatened to target Iran's Pickaxe Mountain, signalling the possibility of further military action against the country.

Speaking during an interview on The Hugh Hewitt Show on Monday, Trump said the heavily fortified site could be the next target of US military action.

"We're going to take out Pickaxe Mountain. Tell the Iranians to be ready," Trump said.

He said the United States had been closely monitoring the facility and claimed there had been little activity there.

"We're watching Pickaxe Mountain closely. We see no activity there. They're not doing well with their nuclear situation. Every time we hear about it, we blow it up. So they don't like talking about it. But we'll probably give Pickaxe a shot relatively soon," he said.

Pickaxe Mountain, located near Iran's Natanz uranium enrichment facility, is believed to house two deeply buried tunnel complexes that defence analysts say are beyond the reach of even the most powerful bunker-buster bombs currently in the US arsenal.

Earlier on Monday, Trump also announced the reinstatement of a US blockade on Iranian shipping in the Gulf. He said Washington would ensure the Strait of Hormuz remains open, adding that vessels would be required to pay a fee to use the strategic waterway.

Trump also warned that additional military strikes against Iran could follow.

"We're going to hit them very hard tonight and we're going to hit them hard tomorrow. And there's not a damn thing they can do about it," he said.