WASHINGTON — For President Trump and two of the allies he values most — Israel and Saudi Arabia — the problem of the Iranian nuclear accord was not, primarily, about nuclear weapons. It was that the deal legitimized and normalized Iran’s clerical government, reopening it to the world economy with oil revenue that financed its adventures in Syria and Iraq, its missile program and its support of terrorist groups.

Now, by announcing on Tuesday that he is exiting the nuclear deal and will reimpose economic sanctions on Iran and companies around the world that do business with the country, Mr. Trump is engaged in a grand, highly risky experiment.

[Read a full transcript of President Trump’s remarks.]

Mr. Trump and his Middle East allies are betting they can cut Iran’s economic lifeline and thus “break the regime,” as one senior European official described the effort. In theory, America’s withdrawal could free Iran to produce as much nuclear material as it wants — as it was doing five years ago, when the world feared that it was headed toward a bomb.

But Mr. Trump’s team dismisses that risk: Iran does not have the economic strength to confront the United States, Israel and Saudi Arabia. And Iran knows that any move to produce a weapon would only provide Israel and the United States with a rationale for taking military action.