By the end of last month, American spy agencies monitoring Israel’s military activities and discussions among the country’s political leadership had come to a striking conclusion: Prime Minister Benjamin Netanyahu was planning for an imminent attack on Iran’s nuclear program, with or without the participation of the United States.

Mr. Netanyahu had spent more than a decade warning that an overwhelming military assault was necessary before Iran reached the point that it could quickly build a nuclear weapon. Yet he had always backed down after multiple American presidents, fearful of the consequences of another conflagration in the Middle East, told him the United States would not assist in an attack.

But this time, the American intelligence assessment was that Mr. Netanyahu was preparing not just a limited strike on the nuclear facilities, but a far more expansive attack that could imperil the Iranian regime itself — and that he was prepared to go it alone.

The intelligence left President Trump facing difficult choices. He had become invested in a diplomatic push to persuade Iran to give up its nuclear ambitions, and had already swatted down one attempt by Mr. Netanyahu, in April, to convince him that the time was right for a military assault on Iran. During a strained phone call in late May, Mr. Trump again warned the Israeli leader against a unilateral attack that would short-circuit the diplomacy.

But over the last several weeks, it became increasingly apparent to Trump administration officials that they might not be able to stop Mr. Netanyahu this time, according to interviews with key players in the administration’s deliberations over how to respond and others familiar with their thinking. At the same time, Mr. Trump was getting impatient with Iran over the slow pace of negotiations and beginning to conclude that the talks might go nowhere.

Contrary to Israeli claims, senior administration officials were unaware of any new intelligence showing that the Iranians were rushing to build a nuclear bomb — a move that would justify a pre-emptive strike. But seeing they would most likely not be able to deter Mr. Netanyahu and were no longer driving events, Mr. Trump’s advisers weighed alternatives.