US President Donald Trump signed an executive order on Monday targeting Iranian Supreme Leader Ayatollah Ali Khamenei and other senior Iranian officials with financial sanctions.

The sanctions follow Iran's downing of a US surveillance drone worth over $100 million over the Strait of Hormuz last week. Trump pulled back from the brink of retaliatory strikes on Iran last week, but appears to be continuing to ratchet up his "maximum pressure" campaign.

The targets of the new sanctions include senior military figures in Iran, blocking their access to any financial assets under US jurisdiction.

"These measures represent a strong and proportionate response to Iran's increasingly provocative actions," Trump told reporters in the Oval Office.

He added that the US would "continue to increase pressure on Tehran until the regime abandons its dangerous activities and its aspirations, including the pursuit of nuclear weapons, increased enrichment of uranium, development of ballistic missiles, engagement and support for terrorism, fuelling of foreign conflicts and belligerent acts directed against the United States and its allies."

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Although Iranian officials have not yet responded to the hard-hitting limitations, the semi-official Tasnim and Fars news agencies have reported that the sanctions are "based on fabricated excuses".

Iranian authorities contacted by Reuters were not immediately available to comment on the move. The sanctions work to deny Supreme Leader Ali Khamenei and his close aides access to money and support.

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Iran's naval commander has warned that Iranian forces will not hesitate to act again and shoot down more US surveillance drones that allegedly violate Iranian airspace. The US claimed that the drone was flying over international waters.

"We confidently say that the crushing response can always be repeated, and the enemy knows it," Rear Admiral Hossein Khanzadi was quoted as saying by Tasnim news agency.