President Hassan Rouhani said Thursday Iran's military power was "purely defensive", after tensions with the United States over its missile programme and a nuclear deal soared following Donald Trump's inauguration.

"The Islamic Republic of Iran has showed that it doesn't intend to interfere with the internal affairs of other countries," Rouhani told foreign diplomats in Tehran, according to the ISNA news agency.

"Our military power is purely defensive," he was quoted as saying.

The comments from Rouhani, a moderate expected to run for re-election later this year, come after the war of words between Iran and the US spiked following Tehran's announcement of a ballistic missile test and Trump's controversial travel ban.

"At the current time, we must not allow some to create an unhealthy climate by conjuring illusions," Rouhani said, quoted by ISNA.

The new US president in his first weeks in office issued an executive order banning travel to the US for nationals of seven predominantly Muslim countries, including Iran.

He has criticised the landmark nuclear deal signed between Iran and world powers -- including the US -- and warned Iran last week it was "playing with fire" following the Islamic republic's missile test on January 29 and military drills last week.

The White House on Friday raised the stakes in the increasingly tense stand-off by slapping fresh sanctions on Tehran's weapons procurement network.

Iranian supreme leader Ayatollah Ali Khamenei on Tuesday that Trump's behaviour showed "the real face of America", long a leading adversary of Tehran.

Defence Minister Hossein Dehghan on Thursday rubbished a report by US cable channel Fox News the day before that alleged Iran had launched a new ballistic missile, Iran's IRNA news agency reported.