WASHINGTON — President Obama on Tuesday rejected an appeal by Prime Minister Benjamin Netanyahu of Israel to spell out a specific “red line” that Iran could not cross in its nuclear program, a senior administration official said, deepening the divide between the allies over how to deal with Iran’s nuclear ambitions.

In an hourlong telephone conversation, this official said, Mr. Obama deflected Mr. Netanyahu’s proposal to make the size of Iran’s stockpile of close-to-bomb-grade uranium the threshold for a military strike by the United States against its nuclear facilities.

Mr. Obama, the official said, repeated the assurances he gave to Mr. Netanyahu in March that the United States would not allow Iran to manufacture a nuclear weapon. But the president was unwilling to agree on any specific action by Iran — like reaching a defined threshold on nuclear material, or failing to adhere to a deadline on negotiations — that would lead to American military action.

“We need some ability for the president to have decision-making room,” said the official, who spoke on the condition of anonymity because of the delicacy of the talks. “We have a red line, which is a nuclear weapon. We’re committed to that red line.”