President Trump made clear on Monday that he was not happy with Israel’s new attacks on Iran, the latest in a string of criticisms that have raised questions about whether the allies are on the same page when it comes to wars that Washington is trying to end.

Iran and Israel traded attacks on Sunday and Monday for the first time since a cease-fire was reached in April. The flare-up showcased just how wide the divide between the American and Israeli leaders has grown since they decided to jointly launch their offensive against Iran in late February.

On Monday, Mr. Trump called in a social media post for both Israel and Iran to “immediately stop” their attacks. And he pressed Prime Minister Benjamin Netanyahu of Israel, in a phone call, to back off on new strikes on Iran, according to a senior U.S. official and two Israeli military officials, speaking on condition of anonymity because they were not authorized to discuss the conversation.

Mr. Netanyahu of Israel was instrumental in persuading Mr. Trump to go to war with Iran, even attending a Situation Room briefing with the president at the White House a few weeks before it began.

Mr. Trump appears to have since soured on the hostilities, insisting anew on Monday that peace negotiations were nearing a resolution, “subject to ignorance or stupidity getting in its way.”

Hasan Alhasan, an expert in Middle East policy at the International Institute for Strategic Studies, said that while Israel influenced Mr. Trump’s decision to go to war with Iran, the president appears so far to have only limited ability to rein in Mr. Netanyahu’s battlefield decisions.

“Trump has actually been quite amenable to Israel’s prodding and pushing, and I think they’ve managed to steer his policy on Iran generally in their favor until it became clear that the proposition that they had sold him wasn’t really going anywhere,” Mr. Alhasan said.

“It’s going to take more than an angry phone call from Trump to really bring about significant behavioral change from Netanyahu’s government,” he added.

Iran attacked Israel on Sunday in retaliation for an Israeli strike the same day on the outskirts of the Lebanese capital, Beirut, a stronghold of Iran-backed Hezbollah. The Israeli attack followed Hezbollah rocket fire from Lebanon into northern Israel.

It was only the third Israeli attack on the Dahiya neighborhood since the U.S. brokered a cease-fire in mid-April.

It is not clear whether the Trump administration condoned Israel’s strikes on Lebanon or Iran over the past two days. But several experts on Monday said they doubted Mr. Trump could have stopped the latest attack on Iran, even if he wanted to.

Israel’s leaders have long described attacks on enemies as acts of self-defense.

While Israel’s defense minister as recently as April suggested that his government was “only waiting for the green light from the U.S.” to bomb Iran into oblivion, Mr. Netanyahu might have gone ahead with Monday’s strikes on Iran even if Mr. Trump opposed it.