WASHINGTON — The White House on Monday redoubled efforts to tout a proposed nuclear deal with Iran as a “forever agreement” that comes with unprecedented transparency, a pledge that remains a hard sale to Israel and Saudi Arabia, the two closest U.S. allies in the Middle East.

Those two countries, the regional powers most preoccupied with Iran’s nuclear ambitions, offered reactions Monday that suggested lingering skepticism.

On the heels of an extensive weekend interview with The New York Times, President Barack Obama taped an interview with NPR in which he hammered home the administration’s message that the deal is unmatched in the scope of inspections, is built on real-life restrictions rather than trust, and that any sanctions relief could be reversed if Tehran doesn’t uphold its end of the agreement.

He also said requiring Iran to recognize Israel would be a “fundamental misjudgment.”

“We want Iran not to have nuclear weapons precisely because we can’t bank on the nature of the regime changing,” he told NPR. “If suddenly Iran transformed itself to Germany or Sweden or France then there would be a different set of conversations about their nuclear infrastructure.”

Energy Secretary Ernest Moniz, who was among the chief negotiators of the nuclear framework last week in the Swiss city of Lausanne, appeared Monday at the White House briefing to address criticism — from home and abroad — that the framework is long on trust and short on details, specifically about whether international inspectors can examine any Iranian nuclear facility at any time.

“This is not built upon trust. This is built upon hard-nosed requirements in terms of limitations on what they do at various time scales and on the access and transparency,” Moniz said.

Israel on Monday listed a set of changes it seeks in a final agreement, including ending research and development work on advanced centrifuges, closing the underground facility at Fordow, disclosing past nuclear developments that could have military dimensions, and allowing inspectors to go anywhere, anytime in Iran to verify the accord.

Yuval Steinitz, Israel’s minister for intelligence and strategic affairs, said the changes would fill gaps that would make the deal “more reasonable.”

But the list of changes was especially notable because it fell well short of Prime Minister Benjamin Netanyahu’s previous demand that Iran’s nuclear program be completely dismantled as an existential threat to Israel. Instead, they appeared designed to counter accusations from Washington that Israel has offered no alternative to the agreement.