US President Donald Trump speaks to reporters before departing from the White House in Washington D.C., the United States, June 22, 2019. Donald Trump on Saturday said that the United States would impose major additional sanctions against Iran on Monday. (Photo: Xinhua)

US President Donald Trump on Tuesday ramped up his rhetoric against Iran by threatening a tough military response in the event of any attack, following fresh US sanctions which were met with tough response from Iran.

"Any attack by Iran on anything American will be met with great and overwhelming force," Trump tweeted on Tuesday.

"In some areas, overwhelming will mean obliteration," he added.

Tensions between Washington and Tehran have intensified after the United States rolled out a new round of sanctions on Monday targeting Iran's Supreme Leader Ayatollah Ali Khamenei and some senior officials, days after the downing of a US military surveillance drone by Iran.

In response, Iranian President Hassan Rouhani said on Tuesday that the White House has a "mental handicap" and vowed that Tehran would not be intimidated by American sanctions, according to media reports.

Iran's Foreign Ministry spokesman Abbas Mousavi said in a tweet on Tuesday that US decision to sanction the Iranian top officials closed the path of diplomacy between Washington and Tehran.

"Trump's administration is destroying all the established international mechanisms developed for maintaining world peace and security," Mousavi added.

Ties between the United States and Iran have deteriorated significantly after Washington walked away from the landmark 2015 Iran nuclear deal in May 2018 and reimposed energy and financial sanctions, which had been removed under the deal, on Iran.

Iran has suspended parts of its commitments subject to the nuclear deal and have threatened to go further.