Mr. Barak’s advocacy for the deal is particularly significant because, as Israel’s defense minister from 2007 to 2013, he led the preparations for a possible military strike against Iran’s nuclear facilities. He warned then that if the Israelis did not act at some point, Iran’s effort to produce a bomb would no longer be vulnerable to any military action.

He and Mr. Netanyahu were closely aligned in that view, but they faced resistance from the chiefs of Israel’s intelligence agencies, who argued that a military strike could have catastrophic consequences and that they were exaggerating the imminence of the Iranian threat.

President Barack Obama implored Mr. Netanyahu to give American efforts at pressure and diplomacy time to work, which he did grudgingly. But the prime minister never liked the resulting agreement. He lobbied against it in the United States Congress and encouraged Mr. Trump to try to renegotiate its terms. (Israel is not part of the deal.)

“Change it, or cancel it,” Mr. Netanyahu said at the United Nations last month. “Fix it, or nix it.”

Under the action being contemplated by the White House, Mr. Trump would essentially kick the agreement to Congress, which would have to decide whether to reimpose sanctions on Iran — a step that would almost certainly blow up the deal — or use the threat of renewed sanctions to try to force the Iranians to renegotiate parts of the agreement.

“Like many Israelis,” Mr. Barak said, “I think the Iran deal is a bad deal. But it is a done deal.”

With the agreement in place, he said, “Iran is far from being an existential threat to Israel.” But he added, “It carries all the potential of turning into an existential threat in the longer-term” — a scenario made more, not less likely, by walking away from the deal, he said.

While refusing to certify the agreement would be politically satisfying for Mr. Trump, Mr. Barak said, it would also not help the United States in its campaign to curb Iran’s ballistic missile program, its support for terrorist organizations, or its cyberwarfare operations.