The new deployment adds to the 2,000 troops the United States has deployed to the Middle East since June as a show of force following a series of Iranian provocations, including attacks on oil tankers in the Persian Gulf and the downing of an American surveillance drone off its coast. Roughly 500 of those troops have gone to Saudi Arabia.

Days after the American surveillance drone was shot down this summer, Mr. Trump approved a limited military strike on Iran — but on June 20 called off the operation at the last minute. Officials said that a covert cyberoperation was carried out instead.

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Earlier Friday, Mr. Trump announced a new round of sanctions against Iran’s national bank, and the administration is said to be considering a range of additional actions, including more cyberattacks. And, at next week’s United Nations General Assembly meeting, Mr. Trump and Mr. Pompeo are expected to press for a diplomatic front against Iran, although many nations — including close allies — hold the administration accountable for rising tensions in the Persian Gulf region following Mr. Trump’s withdrawal from a nuclear deal with Iran.

In describing the new sanctions, Mr. Trump said the move constituted the “highest sanctions ever imposed on a country,” but analysts called it unlikely to inflict substantially more damage to an Iranian economy already suffering from an American economic chokehold.

On the one hand, Mr. Trump volunteered that the United States boasts a “totally renovated” military that includes “new nuclear,” adding, “The nuclear is at a level that it’s never been at before.” Mr. Trump said on Wednesday that he was not considering a nuclear strike on Iran, so it was unclear why he raised the subject of nuclear weapons again on Friday.

He also seemed to revel in his authority to launch a quick strike. Speaking to reporters in the Oval Office alongside the visiting prime minister of Australia, Scott Morrison, he said, “I could do it right here in front of you and that would be it.”