But Israel draws more dire pictures from the same set of facts. In classified exchanges with the United States, it has cited evidence that the design effort secretly resumed in 2005, at the order of Iran’s supreme leader, Ayatollah Ali Khamenei. American officials say that the evidence is circumstantial, and point out that the Israelis have not produced a copy of the order they say Ayatollah Khamenei gave.

”We’re all looking at the same set of facts,” said one senior Israeli intelligence official, who, like others interviewed for this article, asked for anonymity because of the sensitive nature of the intelligence-gathering. “We are interpreting them quite differently than the White House does.”

At the core of the dispute is the “breakout capacity” that Mr. Davies referred to on Wednesday in his first presentation as ambassador to the International Atomic Energy Agency, the United Nations’ nuclear watchdog. The phrase refers to a non-nuclear nation’s ability to acquire enough fuel and expertise to be able to complete building an actual weapon relatively quickly.

The Israelis have argued that there could be little or no warning time  especially if Iran has hidden facilities  and they contended that in the aftermath of Iraq, American intelligence agencies were being far too cautious in assessing Iran’s capability.

As American and Israeli officials expected, Iran turned over to European nations on Wednesday what it called a new set of “proposals” for negotiations over its nuclear program. American officials said they had not read them, but Susan E. Rice, the American ambassador to the United Nations, said the Iranian response must be “serious, substantive and constructive” to meet Mr. Obama’s test.

The White House has given Iran a late-September deadline to begin substantive negotiations, or face additional sanctions.

Image President Mahmoud Ahmadinejad in 2008, touring Irans nuclear operations in Natanz, which Iran says are for electricity. Credit... president.ir

Administration officials are debating whether the Iranian leadership, struggling with violent protests, is effectively paralyzed when it comes to negotiating with the West  or for that matter in determining how aggressively to push ahead with its nuclear program. The White House is hoping its offer to negotiate has thrown Iran’s leadership off track, and built up credibility around the world if the president begins to press for tougher sanctions.