President Trump said in an interview on Sunday afternoon that the agreement he reached with Iran would ultimately assure that the Strait of Hormuz is “permanently toll free” and argued that, despite the objections of Prime Minister Benjamin Netanyahu of Israel, he had saved Israel from nuclear obliteration.

Mr. Trump also insisted that if Iran failed to reach a final nuclear accord with the United States — a process his aides say they expect will begin on Friday in Switzerland — he would restart military attacks on Tehran or make the United States “the guardian of the Middle East” in return for 20 percent of the region’s revenues.

In a 28-minute phone conversation that Mr. Trump initiated from the White House residence, and a brief follow-up call, the president asserted that his decision to attack Iran in late February, and his subsequent naval blockade of its ports after Tehran closed the strait, had remade the Middle East in America’s favor.

Speaking on his 80th birthday, as his family could be heard gathering in the background for a celebratory dinner, he praised two authoritarians — Presidents Xi Jinping of China and Vladimir V. Putin of Russia — for aiding in the settlement, and excoriated Mr. Netanyahu for mounting attacks that nearly derailed the final agreement.

“He’s a very difficult guy,” Mr. Trump said of the Israeli prime minister, “and to be honest with you, he should be very thankful to us for doing this. Because if Iran had a nuclear weapon, Israel wouldn’t be around for two hours.”

While the text of the agreement has not yet been published, Mr. Trump seemed to be describing Iranian concessions that the country has not yet made, or that have been kicked to the follow-up negotiations. The memorandum of understanding, for example, only suspends tolls in the strait for 60 days, and then promises a regional dialogue about the future. Iran had never charged tolls before the war, so Mr. Trump is essentially celebrating a return to the prewar status quo.

Mr. Trump repeatedly compared his new memorandum of understanding to the 2015 agreement reached between President Barack Obama and Iran’s leadership, arguing that his agreement will assure that Iran “cannot develop or purchase a nuclear weapon.” Iran agreed to that when it first ratified the Nuclear Nonproliferation Treaty in 1970, and reaffirmed that agreement on the first page of the Obama-era accord.

Over the past three months of negotiations, led by the president’s special envoy Steve Witkoff and his son-in-law Jared Kushner, the Iranians insisted they would never give up their right to enrich uranium under that treaty. Mr. Trump said they were still negotiating over whether Iran would suspend its enrichment for 20 years — Mr. Trump hinted he might settle for a 15-year suspension — but said Iran would be forever limited to enriching at low levels that “could never be used by the military.”

The Obama administration’s agreement had the same requirement, but Iran began enriching at far higher levels — including near-bomb-grade uranium enriched to 60 percent purity — after Mr. Trump scrapped that deal in 2018.

In the course of the conversation, the president sounded in a celebratory mood, talking about the coming Ultimate Fighting Championship event being held on the South Lawn of the White House and the possibility that it could be interrupted by rain. “This happens in wartime,” he said.