Israelis across the political spectrum have said the agreement appears to leave fundamental security threats posed by Iran unaddressed.

The main headline of Sunday’s Yediot Aharonot, a popular Hebrew daily, summed up in two words the prevailing sentiment in Israel over President Trump’s emerging cease-fire agreement with Iran: “Bad Deal.”

Israel waged two wars against Iran in the past year, the most recent one the campaign launched in late February with U.S. forces. Now Israel, which had not been a party to the Trump administration’s negotiations with Iran, is being left out of the potential peace.

Even before the announcement came on Sunday that a cease-fire agreement had been reached, the details that had surfaced in news media reports prompted a flood of criticism and expressions of discontent from Israelis spanning the country’s political spectrum.

American and Iranian officials have said that under an initial “memorandum of understanding,” Iran would reopen the Strait of Hormuz, a critical shipping route for the global economy, and the United States would lift its blockade on Iranian ports. The cease-fire that the two sides agreed to in April would be extended for 60 days. During that period, both sides would commit to holding detailed negotiations over Iran’s nuclear program, and over the lifting of U.S. sanctions on Iran.

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That would fall far short of the goals that Israel set at the start of the two wars.

At the outset, Prime Minister Benjamin Netanyahu declared that the objective was “to remove the existential threats” to Israel. That meant destroying any nuclear threat from Iran and its ballistic missile program, he said, as well as “creating the conditions” for the Iranian people to topple the government.

The Israelis have also demanded an end to Tehran’s support of its proxy forces hostile to Israel, including Hezbollah in Lebanon and the Houthis in Yemen, as well as support for Hamas in Gaza.

Israeli experts were alarmed that elements key to Israel appear not to have been mentioned at all.

“No matter what will happen, President Trump will declare victory, a total win,” said Jacob Nagel, a former acting national security adviser to Mr. Netanyahu.

“It’s very easy to say what topics” will be up for future negotiations, Mr. Nagel told reporters on Sunday in a video briefing. But, he said, Iran’s ballistic missiles and its support for proxy groups in the region do not even appear as topics in the publicly circulating details.

Mr. Netanyahu’s opponents, commenting before the announcement of the cease-fire, were less charitable.

“A catastrophe from Israel’s perspective,” Avigdor Liberman, a former Israeli defense minister and a right-wing politician, wrote in a social media post on Sunday. Once an ally of Mr. Netanyahu, he is now a bitter critic.

Yair Lapid, the centrist leader of Israel’s parliamentary opposition and a former top government minister, said he hoped the reports about the agreement with Iran were not true. “But if they are,” he said in a statement, “this is one of the most shocking failures of Israel’s foreign and security policy.”

Current Israeli government officials have said little, apparently for fear of upsetting Mr. Trump.

Mr. Netanyahu issued a statement on Friday saying: “As long as I am the prime minister of Israel, Iran will not have nuclear weapons. President Trump and I are in full agreement on this issue.” His statement neglected to mention ballistic missiles or proxy forces.

An Israeli who had been briefed on the deal with Iran, and who requested anonymity to discuss diplomacy, listed Israel’s main problems with the proposal:

• There are no clear answers regarding the treatment of Iran’s stockpile of enriched uranium, and not enough curbs on Iran’s nuclear program, with the deal appearing to rely on Iranian good will.
• Instead of creating the conditions for the collapse of the Iranian government, the deal would allow funds to start flowing back into its coffers.
• The deal lays out no clear mechanism for forcing Iran to halt its support for its proxy forces. But it would mean the suspension of Israel’s campaign against Hezbollah, the militant group it is fighting in Lebanon.

The latest round of fighting in Lebanon erupted after Hezbollah fired at Israel days after the U.S.-Israeli war on Iran began in late February. Iran has insisted that any broader peace agreement extend to the conflict in Lebanon.

Israel has sought to prevent any direct link between a deal with Iran and its military campaign against Hezbollah, noting that the militants are on its doorstep, but its influence appears to have been limited.

With Israeli national elections expected to take place by late October, Mr. Netanyahu is under intense pressure from within his governing coalition and from critics outside the government not to accede to dictates from Mr. Trump. He has been reluctant to oppose Mr. Trump publicly, not least because he has championed their close relationship as one of his main political credentials.

Isabel Kershner, a senior correspondent for The Times in Jerusalem, has been reporting on Israeli and Palestinian affairs since 1990.