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.