Donald Trump's administration has imposed sanctions on Iran following its recent ballistic missile test.
The sanctions target 13 people and 12 companies, including groups in China, Lebanon and the United Arab Emirates.
President Trump tweeted earlier: "Iran is playing with fire - they don't appreciate how 'kind' President Obama was to them. Not me!"
Iran called the threats from "an inexperienced person" useless, vowing to impose reciprocal measures.
John Smith, the US Treasury Department's acting sanctions chief, said in a statement on Friday: "Iran's continued support for terrorism and development of its ballistic missile programme poses a threat to the region, to our partners worldwide and to the United States."
A very different approach - Kim Ghattas, BBC News
President Obama may have sanctioned Iran for its missile test a year ago as well, but President Trump's sanctions come in a very different context and from a very different team.
This administration is filled with officials whose are fixated on Iran, such as National Security Advisor Michael Flynn or Defence Secretary James Mattis.
Mr Obama focused on fostering a tone that wouldn't jeopardise the Islamic Republic's commitment to the nuclear deal. He rarely referred to Iran's paramilitary activities in the region.
But the Treasury Department's mention on Friday of "Iran's malign activity abroad" was a reference to Iranian support for Shia militias and involvement in countries such as Syria and Iraq.
There may be still be echoes of Obama's policies here, but the whole framework of the approach has changed and Mr Trump and his team are signalling clearly they want to cut Iran to size.
Among the newly sanctioned groups are members of the Islamic Republic's Revolutionary Guards Corps.
They are the first Iran sanctions of Mr Trump's new presidency, and come a day after he said "nothing is off the table" in dealing with the country.
Oil prices rose as markets factored in the announcement.
US National Security Adviser Michael Flynn said the US would no longer tolerate Iran's "lawless behaviour" following last Sunday's medium-range missile test.
He said this conduct had only increased since the "very favourable" nuclear deal that six world powers struck two years ago with Iran to halt its nuclear programme.
"The days of turning a blind eye to Iran's hostile and belligerent actions toward the United States and the world community are over," he added.
The White House says the missile launch violated a UN Security Council resolution proscribing missiles that could carry a nuclear device.
Speaking during a visit to Japan on Saturday, US Defence Secretary Jim Mattis said he was not considering increasing the number of US troops in the Middle East to address the Iran issue.
"I don't think it's necessary," he said.
"We have seen [Iran's] misconduct, their misbehaviour, and it's got to be addressed at some point," Mr Mattis added.
But Tehran said it was the US sanctions that breached the UN resolution, which endorsed the 2015 nuclear deal.
Iran's Foreign Minister Mohammad Javad Zarif tweeted on Friday that the Islamic Republic was unmoved by US threats.
"Will never initiate war, but we can only rely on our own means of defence," Mr Zarif wrote.
The Iranian foreign ministry later said Tehran would "impose legal restrictions on a number of American individuals and companies which have been involved in creating and supporting extremist terrorist groups or are helping in the killing and oppression of defenceless people in the region".
It said the names would be announced later.
The Republican Speaker of the US House of Representatives, Paul Ryan, applauded Mr Trump on his administration's "swift and decisive response", in a statement on Twitter.
More than a dozen US senators from both main parties wrote on Thursday to the president, urging "full enforcement of existing sanctions and the imposition of additional sanctions on Iran".
Meanwhile, Saudi Arabia's senior military advisor, Maj Gen Ahmed al Assiri, told the BBC it was time to change Iran's behaviour in the region.
Speaking in the Saudi capital Riyadh, he said Tehran's involvement in neighbouring countries such as Iraq, Syria and Yemen must be stopped.
Gen Assiri, who advises the Saudi defence minister, said Iran must be "brought back to its borders".
Iran - long an arch-foe of Saudi Arabia - says its presence across the region is always at the request of the governments.
The sanctions came as the US moved a Navy destroyer closer to the coast of Yemen to guard waterways from the Iran-aligned Houthi militia, Reuters news agency reports.
Also on Friday, Iran announced a ban against US wrestlers from competing at a championship in the western Iranian city of Kermanshah later this month.
The ban was in response to Mr Trump's executive order temporarily barring travel to the US for Iranian citizens, as well as citizens of six other majority-Muslim countries.