US Defence Secretary James Mattis has called Iran "the world's biggest state sponsor of terrorism", amid rising tensions between the two nations.

His comments come a day after the Trump administration imposed new sanctions against Iran in response to a ballistic missile test.

But Mr Mattis said he did not see any need to boost US troop numbers in the Middle East to deal with Iran.

Iran has been carrying out military exercises in a show of defiance.

The Revolutionary Guards, set up to defend Iran's Islamic government, said the drills would "showcase the power of Iran's revolution and to dismiss the sanctions".

Home-made missile systems, radars, command and control centres, and cyber warfare systems are being tested during Saturday's exercises, state media reported.

A senior commander said the armed forces were ready to "rain down missiles" on the country's enemies if attacked.

"We are working day and night for the security of the Iranian nation," said Amir Ali Hajizadeh, the commander of the Revolutionary Guards' air force.

'Playing with fire'

US officials said the sanctions, targeting 13 people and 12 companies, were in response to last Sunday's missile test and what they called Iran's "continued support for terrorism".

They are the first Iran sanctions of Donald Trump's new presidency, who has signalled a tougher stance on Iran than the Obama administration.

Mr Mattis had more strong words for Iran while visiting Japan.

"As far as Iran goes, this is the single biggest state sponsor of terrorism in the world," he told reporters.

"We have seen their [Iran's] misconduct, their misbehaviour, from Lebanon and Syria to Bahrain and to Yemen and it's got to be addressed at some point," he added.

But he went on to say that despite the recent tensions he saw no need to boost troop numbers in the Middle East.

"We always have the capability to do so, but at this time I don't think it's necessary," he said.

'We will never initiate war'

Iran has denied that its missile test violates a UN Security Council resolution or the nuclear deal it struck with international powers, including the UN.

In response to the US sanctions, Iran announced restrictions against US companies and individuals "involved in creating and supporting extremist terrorist groups or are helping in the killing and oppression of defenceless people".

Iran's Foreign Minister Mohammad Javad Zarif has also said the Islamic Republic was unmoved by US threats.

"We'll never initiate war, but we can only rely on our own means of defence," Mr Zarif wrote.

US officials have suggested more action could follow. Mr Trump has been a vocal critic of the nuclear accord, which saw Iran agreeing to curb its sensitive nuclear activities in return for the lifting of economic sanctions.

Iran is also among the seven Muslim-majority countries included in a controversial US travel ban.