Adding to threats of military action, Trump announced any country doing business with Iran will face a new tariff of 25 per cent on its exports to the US
"This Order is final and conclusive," he said in a social media post.
While the president provided little detail, the move may have more symbolic than practical effect since Iran, a major oil producer, already faces extensive US and international trade sanctions.
Top export destinations for Iran include China, the United Arab Emirates and India.
US Vice President JD Vance, Secretary of State Marco Rubio and key White House National Security Council officials began meeting on Friday to develop a "suite of options", from a diplomatic approach to military strikes, to present to Trump in the coming days, according to a US official familiar with the internal administration deliberations.
Trump has said the US may meet Iranian officials and he was in contact with Iran's opposition, while piling pressure on its leaders over lethal violence against protesters.
Iran's leaders, their regional clout much reduced, are facing fierce demonstrations that evolved from complaints about dire economic hardships to defiant calls for the fall of the deeply entrenched clerical establishment.
US-based rights group HRANA said by late Monday it had verified the deaths of 646 people, including 505 protesters, 113 military and security personnel and seven bystanders, and was investigating 579 more reported deaths.
Since the protests began on December 28, 10,721 people have been arrested, the group said. Reuters was unable to confirm the figures independently.
While airstrikes were one of many alternatives open to Trump, "diplomacy is always the first option for the president", White House press secretary Karoline Leavitt told reporters.
Iranian Foreign Minister Abbas Araqchi said Tehran was studying ideas proposed by Washington, though these were "incompatible" with US threats.
"Communications between (US special envoy Steve) Witkoff and me continued before and after the protests and are still ongoing," he told Al Jazeera.
The flow of information from the Islamic Republic has been hampered by an internet blackout since Thursday, although some Iranians still have access to the internet via Elon Musk's Starlink satellite service, three people inside the country said.
Iran's Ministry of Intelligence said on Monday it had detained "terrorist" teams responsible for acts including killing paramilitary volunteers loyal to the clerical establishment, torching mosques and attacking military sites, according to a statement carried by state media.
Addressing a large crowd in Tehran's Enqelab Square on Monday, parliament speaker Mohammad Baqer Qalibaf said Iranians were fighting a war on four fronts - "economic war, psychological warfare, military war against the US and Israel, and today a war against terrorism".
Declaring the situation "under total control", Araqchi said on Monday 53 mosques and 180 ambulances had been set on fire since the protests erupted.
Trump said on Sunday Iran had called to negotiate about its disputed nuclear program. Israel and the US bombed Iranian nuclear sites in a 12-day war in June.
"A meeting is being set up, but we may have to act because of what is happening before the meeting," he told reporters on Air Force One.
Trump was to meet with senior advisers on Tuesday to discuss options for Iran, a US official told Reuters.
The Wall Street Journal reported that those included military strikes, using secret cyber weapons, widening sanctions and providing online help to anti-government sources.
In an interview with CBS News, Reza Pahlavi, son of Iran's last shah who lives in exile in the US, urged Trump to intervene "sooner".
With AP
