Any prospect of easing tensions between the United States and Iran seemed increasingly remote Tuesday, as threats and personal insults flew between the two governments.

In language reminiscent of last year’s taunts between President Trump and North Korea’s Kim Jong Un, Iranian President ­Hassan Rouhani described the White House as “mentally crippled” and denounced new sanctions against Iran’s supreme leader, Ayatollah Ali Khamenei, as “outrageous and idiotic.”

Trump called Rouhani’s comments “ignorant” and said that Iran does “not understand reality.” Any attack on “anything American,” tweeted the president — who last week called off a military strike that was to have been launched after Iran shot down a U.S. drone — will bring “overwhelming” U.S. force and “obliteration” of some Iranian assets.

Beneath the din, no new options emerged for avoiding a conflict that both sides say they do not want, and more doors appeared to be closing rather than opening.

Iran shot down a U.S. drone near the Strait of Hormuz on June 20, escalating tensions. Each country has different accounts about the location of the incident. (Joyce Lee, William Neff/The Washington Post)

Trump has said repeatedly that he wants to talk. But he has indicated he is prepared to continue squeezing the Iranian economy and leadership until Iran meets the “very simple demands” he has tweeted — “No Nuclear Weapons and No Further Sponsoring of Terror!”

Iran, whose nuclear energy program is under international restrictions, says that it sees no reason to talk with an adversary that is crushing the life out of it, and that the United States must first show some respect. It said that “useless sanctioning” of Khamenei and Foreign Minister Mohammad Javad Zarif“means the permanent closure of the doors of diplomacy.”

In Washington, even those who fully and vocally support the administration’s “maximum pressure” sanctions policy have begun to question whether Trump has a strategy.

Mark Dubowitz, chief executive of the Foundation for Defense of Democracies, pushed back at critics who said economic sanctions against Khamenei were merely “symbolic” because the ayatollah has no U.S. assets. As the head of an authoritarian state, Khamenei presides over a $200 billion corporate conglomerate that controls massive international investments, Dubowitz said in a Twitter post.

But it was “perfectly legitimate,” Dubowitz tweeted, “to ask what impact [the Khamenei sanctions] will have on U.S.-Iran diplomacy.”

Michael Rubin, a Middle East expert at the American Enterprise Institute, where he worked with Trump national security adviser John Bolton, said, “I’m one who believes that pressure can work” against Iran. But neither the Iranians nor many of Trump’s own supporters understand where Trump is heading, he said.

“During the campaign, Trump talked about how a lack of predictability can actually be a strategic asset,” Rubin said. “But that presupposes that the lack of predictability is part of a policy rather than cover for lack of a policy.”

“We’re at a very dangerous point right now where we risk allowing the Iranian leaders to rally people around the flag. In other words, sometimes it’s better to address a problem with a scalpel rather than an ax,” he said.

Other experts said that Trump’s summit strategy with nuclear-armed North Korea, in which both leaders had reason to seek the public spectacle of a meeting, but whose governments have yet to substantively address their differences, would not work with Iran.

“When and if Tehran is ready to talk, the differences between Trump and Khamenei present further obstacles,” said Karim Sadjadpour of the Carnegie Endowment for International Peace. “Trump prefers public pageants about broad topics; Khamenei prefers private discussions about narrow topics.”

While Trump has emphasized that Iran’s military forces would be no match for those of the United States, U.S. defense officials have wondered whether provoking a confrontation is wise, and whether Bolton, a leading hawk on Iran, is pushing the president into a position where conflict is the only option.

Trump has been on all sides of the issue. After last week’s drone shoot-down, he warned that Tehran had made a “big mistake” but later speculated that the attack was the errant action of low-level personnel. From first authorizing a retaliatory strike, to calling it off because it might cause “disproportionate” Iranian deaths, he arrived at Tuesday’s threat that “any attack by Iran on anything American will be met with great and overwhelming force,” and in some cases “obliteration.”

Asked Tuesday whether he had an exit strategy in the event of war, Trump told reporters, “You’re not going to need an exit strategy. I don’t do exit strategies.”

Sadjadpour said that “the danger of Trump’s approach is that he’s provoked an escalatory cycle while also signaling to Iran and the world that he has no interest in conflict. As a result, Tehran may miscalculate that it can continue to take free shots against U.S. interests, allies and assets.”

Lawmakers have focused their attention on the legal authority that might be used to conduct military action against Iran. Democrats in both houses of Congress want to amend the defense bill to state unequivocally that Trump would have to seek congressional authorization before engaging militarily with Iran. Some in the Senate advocate blocking the defense legislation until they are promised a vote on Iran.

“There’s a lot of folks who think we need to take a stand,” said Sen. Chris Murphy (D-Conn.), emerging from a meeting of Senate Democrats in which there was significant discussion of what they should do.

As Democrats huddled, Senate Majority Leader Mitch McConnell (R-Ky.) told reporters that while he would personally oppose the amendment, “I am not opposed to having the vote.”

Pentagon officials do not think that Congress’s 2001 Authorization for the Use of Military Force in response to the Sept. 11, 2001, al-Qaeda attacks in this country — the foundation for virtually every U.S. military action since then in the Middle East, North Africa and Asia — can be used as a legal basis for war with Iran, said a defense official who spoke on the condition of anonymity to comment on the sensitive issue.

Any dispute over the authorization issue is likely to be moot. Trump has said he thinks he has all the authority he needs to strike Iran, and the likelihood is that the president would declare such action authorized under his constitutional power to act in the nation’s defense.

But Republican leaders, including McConnell, expressed concern over the debate itself, saying that if Congress appeared to be trying to limit the president’s actions, the international community would be further confused about U.S. policy.

Confusion, however, already appears rampant, along with mistrust of the administration.

Secretary of State Mike Pompeo, in response to questions raised by allies, experts and journalists about whether the U.S. drone was over international waters when it was shot down — as the administration said — or within Iran’s maritime boundaries, as Tehran insisted, implied Sunday that expressing doubt was tantamount to aiding an adversary.

The “childlike map” presented by Zarif, the Iranian foreign minister, was a clear “contrast with the excellence and professionalism of America’s military and intelligence services,” Pompeo said. “We shouldn’t let the Iranians have one moment where any reporter would write there is even a credible response to the data set that the Americans have put forward.”

Pompeo accused Iran of additional “disinformation,” including what he said were reports last week that the United States was withdrawing from a military base in Iraq, although the report in question, by Reuters, was attributed to U.S. military officials and referred only to the withdrawal of contractors.

Retired U.S. diplomat Jeffrey Feltman, a Middle East expert who served in numerous senior State Department posts and as undersecretary for policy at the United Nations, said that “rhetoric aside,” Iran has taken steps — including the drone shoot-down — “to make sure that we know that they will react to American steps.” But Iran has not taken “such big steps as to be irreversible, assuming no miscalculation and no misinterpretation. . . . Nor, for that matter, have we,” he said of the Trump administration.

“But at some point, it just seems like this becomes increasingly risky,” Feltman said. “The idea of relying on the Iranian mullahs for restraint or on the president’s instincts not to go to war, I think those are pretty weak foundations on which to build a de-escalation strategy.”

Karoun Demirjian and Missy Ryan in Washington, Erin Cunningham in Dubai and Ruth Eglash in Jerusalem contributed to this report.