With tensions running high between the two countries, Trump signed an executive order imposing the sanctions, which US Treasury Secretary Steven Mnuchin said would lock billions of dollars more in Iranian assets.
Trump said the new sanctions were in part a response to last week's downing of a US drone, but would have happened anyway. He said the supreme leader was ultimately responsible for what Trump called "the hostile conduct of the regime."
"Sanctions imposed through the executive order ... will deny the Supreme Leader and the Supreme Leader's office, and those closely affiliated with him and the office, access to key financial resources and support," Trump said.
The Trump administration wants to force Tehran to open talks on its nuclear and missile programs and its activities in the region. Tensions between the United States and Iran have grown since May when Washington ordered all countries to halt imports of Iranian oil.
There was no immediate reaction in Iranian official media but at the weekend, state-run news agency IRIB quoted Foreign Ministry spokesman Abbas Mousavi as saying any new sanctions would be "just propaganda" and "there are no more sanctions left."
Mnuchin said Iranian Foreign Minister Mohammad Javad Zarif would be targeted with US sanctions later this week.
Sanctions were also imposed on eight senior commanders of Navy, Aerospace, and Ground Forces of the Islamic Revolutionary Guards Corps (IRGC), the US Treasury Department said.
"These commanders sit atop a bureaucracy that supervises the IRGC’s malicious regional activities, including its provocative ballistic missile program, harassment and sabotage of commercial vessels in international waters, and its destabilizing presence in Syria," the department said in a statement.
Trump said the sanctions are a "strong and proportionate response to Iran's increasingly provocative actions."
"We will continue to increase pressure on Tehran until the regime abandons its dangerous activities and its aspirations," he said.
Iran said on Monday US cyber attacks on its military had failed, as Washington sought to rally support in the Middle East and Europe for a hardline stance that has brought it to the verge of conflict with its longtime foe.
MARITIME SECURITY
Washington has blamed Tehran for attacks on tankers in the Gulf in recent weeks, which Iran denies. On Monday, the United States said it was building a coalition with allies to protect Gulf shipping lanes.
A coalition of nations would provide both material and financial contributions to the program, a senior US State Department official said, without identifying the countries.
"It's about proactive deterrence, because the Iranians just want to go out and do what they want to do and say hey we didn't do it. We know what they've done," the official told reporters, adding that the deterrents would include cameras, binoculars and ships.
The United States accuses Iran of encouraging allies in Yemen to attack Saudi targets.
In a joint statement on Monday, the United States, Saudi Arabia, the UAE and Britain expressed concern over Middle East tensions and the dangers posed by Iranian "destabilizing activity" to peace and security in Yemen and the region.
The confrontation between Iran and the United States heated up last Thursday when Iran shot down an American drone, saying it had flown over its air space.
Washington, which said the drone was in international skies, then appeared to come close to attacking Iranian military targets, with Trump saying that he aborted a retaliatory air strike 10 minutes before it was to go ahead.
Trump said he decided the strike, to punish Iran for shooting down the drone, would have killed too many people.
US media have reported that Washington launched cyber attacks last week even as Trump called off his air strike. The Washington Post said on Saturday that the cyber strikes, which had been planned previously, had disabled Iranian rocket launch systems. US officials have declined to comment.
FEARS OF WAR
Iran dismissed the cyber attacks as a failure.
"They try hard, but have not carried out a successful attack," Mohammad Javad Azari Jahromi, Iran's minister for information and communications technology, said on Twitter.
Allies of the United States have been calling for steps to defuse the crisis, saying they fear a small mistake by either side could trigger war.
"We are very concerned. We don't think either side wants a war, but we are very concerned that we could get into an accidental war and we are doing everything we can to ratchet things down," British Foreign Secretary Jeremy Hunt said.
US Secretary of State Mike Pompeo jetted to the Middle East to discuss Iran with the leaders of Saudi Arabia and the United Arab Emirates, two Gulf Arab allies that favor a hard line. Pompeo met King Salman as well as the king's son, de facto ruler Crown Prince Mohammed bin Salman.
The US special representative for Iran, Brian Hook, visited Oman and was headed to Europe to explain US policy to allies. He told European reporters on a phone call ahead of his arrival that Trump was willing to sit down with Iran, but that Iran must do a deal before sanctions could be lifted.
CONCESSIONS
US-Iran relations have deteriorated over the past year since the United States abandoned a 2015 agreement between Iran and world powers designed to curb Iran's nuclear program in return for the lifting of sanctions.
US allies in Europe and Asia view Trump's decision to abandon the nuclear deal as a mistake that strengthens hardliners in Iran and weakens the pragmatic faction of President Hassan Rouhani.
France, Britain and Germany have sent an official diplomatic warning to Iran if Tehran reduces its compliance with the accord, two European diplomats said on Monday.
It was not immediately clear what consequences Iran might face for non-compliance.
Washington argues that the agreement known as the JCPOA, negotiated under Trump's predecessor, President Barack Obama, did not go far enough, and new sanctions are needed to force Iran back to the table to make more concessions.
Both sides have suggested they are willing to hold talks while demanding the other side move first. In the latest comment from Tehran, an adviser to Rouhani repeated a longstanding demand that Washington lift sanctions before any talks.
But the adviser, Hesameddin Ashena, also tweeted a rare suggestion that Iran could be willing to discuss new concessions, if Washington were willing to put new incentives on the table that go beyond those in the deal."If they want something beyond the JCPOA, they should offer something beyond the JCPOA; with international guarantees."