DUBAI, United Arab Emirates - President Donald Trump on Tuesday warned Iran that any attack on "anything American" would be met with "great and overwhelming force" following Iranian remarks slamming new U.S. sanctions as permanently closing the path to diplomacy amid a spike in tensions in the Persian Gulf.

Iran's leadership "doesn't understand the words 'nice' or 'compassion,' they never had," Trump said in a series of tweets.

"Sadly, the thing they do understand is Strength and Power," he said. "Any attack by Iran on anything American will be met with great and overwhelming force. In some areas, overwhelming will mean obliteration!"

Iranian officials earlier Tuesday criticized new penalties targeting Iran's supreme leader, Ayatollah Ali Khamenei, saying that the White House had "become mentally crippled."

In a searing televised address, Iranian President Hassan Rouhani called restrictions against Iran's supreme leader "outrageous and idiotic" and said they showed "certain failure" on the part of the Trump administration to isolate Iran.

Trump called Rouhani's comments "ignorant and insulting," saying that they only showed that Iran does "not understand reality."

"You call for negotiations. If you are telling the truth, why are you simultaneously seeking to sanction our foreign minister?" Rouhani said Tuesday, referring to remarks by U.S. officials suggesting plans to sanction Foreign Minister Mohammad Javad Zarif later this month.

Iran's Foreign Ministry spokesman said on Twitter that the "useless sanctioning" of Supreme Leader Ali Khamenei and Zarif, who led Iran's nuclear negotiations with world powers, "means the permanent closure of the doors of diplomacy."

"Trump's government is annihilating all of the established international mechanisms for maintaining world peace and security," said the spokesman, Abbas Mousavi.

Trump announced the measures Monday, which U.S. officials said came in response to the downing of a U.S. Navy surveillance drone over the Strait of Hormuz last week. The sanctions also targeted senior commanders of Iran's Islamic Revolutionary Guard Corps, including those the Treasury Department said were involved in shooting down the drone, a RQ-4A Global Hawk.

The United States has also blamed Iran for a recent string of attacks on petrochemical tankers in the Persian Gulf region. Iran has denied involvement.

Rouhani said Tuesday that the sanctions against Khamenei - whom Trump described as "the one who is ultimately responsible for the hostile conduct of the regime" - were futile because the 80-year-old leader does not maintain any financial assets abroad.

"Tehran's strategic patience does not mean we have fear," he said.

National security adviser John Bolton described the new economic penalties Tuesday as "significant" but said that Trump has also "held the door open to real negotiations" with Iran.

"All that Iran needs to do is walk through that door," Bolton said at a conference in Jerusalem. He added that any deal would need to "eliminate Iran's nuclear weapons program, its pursuit of ballistic missile delivery systems, its support for international terrorism and other malign behavior worldwide."

Iran does not have a nuclear weapons program and has complied with restrictions to its atomic energy activities set out under the 2015 deal it negotiated with world powers, including the United States.

The Trump administration abandoned that pact and reimposed a near-total embargo on Iran's economy, including its oil, shipping, manufacturing and banking industries.

Iran said last week that it was on course to boost its stockpile of low-enriched uranium beyond the limits prescribed by the deal, a move that arms control experts said does not pose a near-term proliferation risk.

Zarif said Tuesday from Tehran that Iran would "never seek a nuclear weapon based on its religious and strategic views," the Fars News Agency reported.

The head of Iran's Supreme National Security Council, Ali Shamkhani, said Tuesday, however, that a decision was made to further modify Iranian commitments to the nuclear deal. In a "memo" he wrote to the Fars News Agency, Shamkhani did not elaborate on the specific steps Iran would take.

The 2015 agreement curbed Iran's nuclear energy program in exchange for widespread sanctions relief. But the deal's other signatories, including the European Union, have struggled to maintain the economic benefits promised to Iran under the pact.

After a meeting with his counterparts, Bolton told reporters that the U.S. pressure campaign would force Iran to engage in new nuclear negotiations, Reuters news agency reported.

"They'll either get the point or . . . we will simply enhance the maximum-pressure campaign further," Bolton said. He predicted that "the combination of sanctions and other pressure" would "bring Iran to the table."

A Russian participant in the Jerusalem conference, Nikolai Patrushev, secretary of Russia's Security Council, told reporters Tuesday that Russia has military intelligence showing that the U.S. drone was in Iranian airspace when it was shot down by Iran last week, Reuters reported. Patrushev also described U.S. evidence that Iran was behind attacks on ships in the Gulf of Oman as poor quality and unprofessional.

Trump has said that he is willing to speak to Iran with no preconditions, but U.S. officials said this week that there is currently no back channel between the U.S. and Iranian governments. And planned sanctions against Iran's chief diplomat undermined the administration's message that it seeks unconditional talks with Iranian officials.

"If Zarif is sanctioned, it won't be to punish him because of his service to the Islamic Republic," said Esfandyar Batmanghelidj, founder of the Europe-Iran forum that promotes business ties between Iran and European nations.

"It will be because of his own dogged commitment - to diplomacy - and of his proven ability to keep the door open for negotiations despite the sabotaging by rivals in both Tehran and Washington," he said.

This article was written by Ruth Eglash and Erin Cunningham, reporters for The Washington Post. Eglash reported from Jerusalem. Eglash reported from Jerusalem. The Washington Post's Carol Morello and Missy Ryan contributed to this report.