The United States is always an outsize player abroad, its statements often carrying more effect in foreign lands than at home. But Mr. Trump’s use of bald threats and warnings of military intervention have accelerated the laws of unintended consequences.
“No one should be allowed to decide on a military action on the Korean Peninsula without South Korean agreement,” Mr. Moon said, executing exactly the kind of split between Seoul and Washington that Kim Jong-un, the North Korean leader, has long sought.
His declaration underscored how Mr. Trump’s language, which took White House aides by surprise, is sowing division with an ally whose help would be vital to the success of any American military campaign on the divided peninsula.
South Koreans have seen a lot of tensions with Washington, but they have never seen an American president explicitly threaten the North with talk of “fire and fury like the world has never seen,” or a declaration that American forces are “locked and loaded” for a conflict.
“The Americans had always been an ally who would prevent, not start, war on the Korean Peninsula,” said Kim Ji-woon, a college student attending a rally on Monday in central Seoul that featured a large banner reading, “Trump, shut up!”
“With his trash war talk,” the student said, “Trump makes me wonder what’s the use of the alliance.”
Mr. Moon has been careful to avoid any steps that his conservative enemies could use to accuse him of undermining the South’s relationship with the United States. But all South Korean leaders have learned that it is politically untenable to look too weak to stand up to a bigger power, even if it happens to be the country’s main ally.
Many South Koreans have seethed in recent days over other comments by Senator Lindsey Graham, Republican of South Carolina, about how a conflict with the North would play out.
“If thousands die, they’re going to die over there — they’re not going to die here,” Mr. Graham said on NBC’s “Today” show, adding that Mr. Trump shared that view and was willing to use military force if necessary. “He’s told me that to my face — and that may be provocative, but not really. When you’re president of the United States, where does your allegiance lie?”
Iran poses a different issue. Mr. Trump has made clear he would like to exit from the Iran deal as fast as he can, though he has never publicly discussed how that could pave the way for Iran to resume producing uranium and plutonium at levels that could be diverted to weapons use. Some in Iran’s Revolutionary Guards Corps would also like to see the deal collapse, so they can resume their nuclear activities.
Mr. Rouhani has no interest in watching the agreement dissolve: It is the core of Iran’s new economic relationship with Europe, Russia and China. If the country raced again to produce near-bomb-grade fuel, an international movement could well arise to reimpose sanctions, unless Iran could successfully argue that Mr. Trump goaded the country into its actions.
But Mr. Rouhani’s statements to Iranian lawmakers were driven by a domestic imperative not to be seen giving in to American threats to pull out of the deal or renegotiate or widen it.
Mr. Rouhani’s warning was immediately taken up by the Trump administration. Nikki R. Haley, the American ambassador to the United Nations, said in a statement that the warning amounted to an Iranian attempt at blackmail.
“Iran cannot be allowed to use the nuclear deal to hold the world hostage,” Ms. Haley said in the statement.
The new United States sanctions on Iran, she said, were not a violation of the nuclear deal but part of an effort to “hold Iran responsible for its missile launches, support for terrorism, disregard for human rights and violations of U.N. Security Council resolutions.”
Several other Iranian officials have recently threatened to restart industrial-scale uranium enrichment. Ali Akbar Salehi, the president of the Atomic Energy Organization of Iran and a key negotiator of the deal, said the country could go up to 20 percent enrichment of uranium to “surprise the Americans and their supporters.” While that level does not produce bomb-grade material, it is close — and when Iran began enriching uranium at 20 percent several years ago, it triggered one of the crises that led to threats of conflict and, ultimately, the negotiation over the nuclear deal.
Mr. Maduro’s move to rally Venezuela behind new military exercises seemed driven by a desire to remind Venezuelans of previous eras in which the United States meddled in Latin America. The country’s defense minister, Vladimir Padrino, warned that the United States sought the nation’s oil supplies, an accusation straight out of the history books.
Vice President Mike Pence, in a speech on Monday, struck a more conciliatory note, saying that a diplomatic approach must be employed to stop the country’s slide into authoritarian rule.
Mr. Trump, he said in a visit to Colombia, “made it very clear that we will not stand by while Venezuela collapses into dictatorship.”
“A failed state in Venezuela threatens the security and prosperity of our entire hemisphere and the people of the United States of America.” But Mr. Pence never explained what, if any, military solution to the problem was available.
His hosts bristled at Mr. Trump’s threat. “The possibility of a military intervention shouldn’t even be considered,” President Juan Manuel Santos of Colombia said during Mr. Pence’s visit.
An earlier version of this report incorrectly attributed a quote to President Trump. In fact, it was President Moon Jae-in of South Korea who said that “No one should be allowed to decide on a military action on the Korean Peninsula without South Korean agreement.”
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