Two days after subjecting Iran to a Twitter bombardment, US President Donald Trump said he remained eager to negotiate a new nuclear deal with Tehran.

"We'll see what happens, but we're ready to make a real deal, not the deal that was done by the previous administration, which was a disaster," Trump said on July 24 in a speech to veterans in the US state of Missouri.

In his tweeted outburst, Trump threatened Tehran with "consequences the likes of which few throughout history have ever suffered before". It was thought to be a response to Iranian President Hassan Rouhani warning Trump not to "play with the lion's tail".

The US will throughout the remainder of this year crank up a campaign of heavy sanctions designed to force Tehran to the table to renegotiate the nuclear deal and its role in Middle East affairs.

US Defence Secretary Jim Mattis on July 24 declined to comment directly on Trump's threats against Iran. However, he outlined his concerns about Iranian actions in the Middle East, including Tehran's support for Syrian President Bashar al-Assad and the Houthi rebels fighting the government in Yemen. That conflict is seen as a proxy war between Iran and Saudi Arabia.

"I think the president was making very clear that they're [the Iranians] on the wrong track," Mattis said on a visit to California.

"It's time for Iran to shape up and show responsibility as a responsible nation. It cannot continue to show irresponsibility as a revolutionary organisation that is intent on exporting terrorism, exporting disruption, across the region."

Iran takes issues with US claims that it exports terrorism.