Trump called statements made by Iranian President Hassan Rouhani and a spokesperson for Iran's foreign minister "ignorant and insulting," and then -- after brandishing U.S. military power -- issued a stark threat: "Any attack by Iran on anything American will be met with great and overwhelming force. In some areas, overwhelming will mean obliteration."
The president said Iranian leadership doesn't "understand the words "nice" or "compassion." "Sadly, the thing they do understand is Strength and Power, and the USA is by far the most powerful Military Force in the world," he added.
"Whatever they want to do, I'm ready," Trump said at an afternoon photo-op. "We cannot allow Iran to have a path to nuclear weapons," he said, after saying he's "not going to need an exit strategy."
Last week, Trump pulled back on a military strike against Iran for shooting down an American surveillance drone, saying he would impose more sanctions, which he announced on Monday, including ones targeting Iran's supreme leader and other top officials in the the Iranian regime.
The president's tweets came hours after Iranian President Hassan Rouhani said at a medical conference that the United States' sanctions against Iran are a "failure," and said "the White House is afflicted by mental retardation and does not know what to do."
Iran’s Foreign Ministry spokesman Abbas Mousavi tweeted that the sanctions against Supreme Leader Ali Khamenei and Iran's Foreign Minister Mohammad Javad Zarif means a "permanent closure of diplomacy." The president signed sanctions against Iranian leaders on Monday in the Oval Office, and the president said he planned to sanction Zarif by the end of the week. Treasury Secretary Steven Mnuchin said that the sanctions target Khamenei and Iranian military leaders who were connected to the downing of a U.S. military drone over the Strait of Hormuz last week and people connected to the recent attack on oil tankers in the region.
National Security Adviser John Bolton said that he spoke to the president before the tweets were sent out. "He asked me to get the message out," Bolton said.
But at a news conference in Israel on Tuesday, Bolton said that despite the sanctions, the United States still welcomes negotiations with Iran if they plan to "completely and verifiably" eliminate its nuclear weapons program, ballistic missile systems and support for terror networks.
"All that Iran needs to do is to walk through that open door," Bolton said.
Secretary of State Mike Pompeo, during an unannounced visit to Kabul, Afghanistan called the comments from President Rouhani "immature and childlike."
"But know that the United States will remain steadfast in undertaking the actions that the president laid out in his strategy to create stability throughout the Middle East, which includes the campaign we have, the economic campaign, the pressure campaign that we have on the Islamic Republic of Iran," he said.
ABC News' Conor Finnegan contributed to this report.