The additional sanctions are in response to Iran's ballistic missile test on Sunday. They are similar to actions taken by former President Barack Obama after Iran's previous ballistic missile tests.
In a letter to Trump Thursday, a bipartisan group of senators said, "Iranian leaders must feel sufficient pressure to cease deeply destabilizing activities, from sponsoring terrorist groups to continued testing of ballistic missiles."
"Full enforcement of existing sanctions and the imposition of additional sanctions on Iran for its ballistic missile program are necessary," the letter said.
On Thursday, Trump declined to rule out the prospect of military action against the Islamic Republic.
"Nothing's off the table," he said.
On Friday, Iran's Foreign Minister Javad Zarif took to Twitter, saying Iran was "unmoved" by Trump's threat.
"We'll never initiate war," he said in a tweet. "We will never use our weapons against anyone, except in self-defense. Let us see if any of those who complain can make the same statement."
Trump National Security Adviser Michael Flynn condemned Wednesday Iran's recent ballistic missile test launch
, calling it a "provocative" breach of a UN Security Council resolution. Iran denies that's it's violated any UN mandate.
"As of today, we are officially putting Iran on notice," Flynn said from the White House briefing room.
Speaking to reporters Thursday in Tehran, the Iranian adviser, Ali Akbar Velayati, dismissed what he called the US leader's "baseless ranting" and said that even Americans were not satisfied with "Trump's extremism," according to Iran's semi-official Fars News Agency.
Velayati blasted Trump as lacking sufficient experience, saying he should take lessons from his predecessor, Barack Obama. He added that those who threaten the Muslim world should take a look at US failures in Afghanistan, Iraq and Syria.
He also said that all test-fired missiles were defensive and that Iran did not need to seek permission to carry out such activities.
Nuclear deal threatened
The sudden escalations of US-Iranian tensions have raised concerns about the future of the nuclear accord with Iran, which put stringent limits on the country's nuclear program. It allowed sanctions to be eased and business with Iran to recommence.
Trump has been a longtime critic of the accord, which was brokered after two years of talks with the five members of the Security Council and Germany in 2015.
Flynn on Wednesday did not say whether the United States would take action beyond a verbal warning. Three senior administration officials, speaking on background, said they were still in the early stages of determining what action the United States should take in response.
"We are considering a whole range of options. We're in a deliberative process," one official said.
Nasser Hadian, a professor of international relations at Tehran University, told CNN it was unlikely the Trump administration would tear up the agreement, but it was possible it would impose fresh sanctions on the country.
Abandoning the accord "would serve hard-line interests in Iran," he said.