“We know that the Iranians see red,” Mr. Oren said. “We know they can discern the color red. We know that the redder the line, the lesser the chance that they will pass it.”

Mrs. Clinton publicly rejected that approach over the weekend. In an interview with Bloomberg Radio, she avoided discussion of Iran’s stockpile and said, “We’re not setting deadlines” for military action. It was that statement that appeared to have set off Mr. Netanyahu.

Mr. Obama has repeatedly argued — with the support of some leading Israeli officials — that the United States and Israel have closer security cooperation now than at any other point in history. The United States provided much of the Iron Dome missile defense system for Israel, and for the past five years the two countries worked closely on a major covert operation against Iran called “Olympic Games,” an effort to sabotage Iran’s enrichment capability with cyberattacks.

But Mr. Obama has stopped well short of saying he would prevent Iran from developing the capability to produce a bomb. He has said only that he would not allow Iran to obtain a weapon; Mr. Netanyahu has said that is not enough.

Depending on how one defines the term, Mr. Obama’s aides and former aides acknowledge that Iran may already have that capability. It possesses the fuel and the knowledge to make a weapon, but that would take months or years, and Mr. Obama has argued that allows “time and space” for a negotiated solution.

Mr. Romney had no immediate comment about Mr. Netanyahu’s challenge to Mr. Obama, and one of his informal advisers on the Middle East said, “It’s probably better at this point to let Netanyahu make the point because it’s more powerful that way.” The adviser said he was not authorized to speak on the record.

But the Netanyahu comments play right to the Republican nominee’s critique of Mr. Obama. On “Meet the Press” on Sunday, Mr. Romney declared that the progress of Iran’s nuclear program was Mr. Obama’s “greatest failure” in foreign policy.