But the arguments in front of the president himself were relatively brief, officials said, apparently because so many senior aides objected. Mr. Carter argued that President Vladimir V. Putin of Russia and Kim Jong-un, the North Korean leader, could interpret a promise of no first use as a sign of American weakness, even though that was not the intent.

The defense secretary’s position was supported by Mr. Kerry and Mr. Moniz, two architects of the Iran nuclear deal, who cautioned that such a declaration could unnerve American allies already fearful that America’s nuclear umbrella cannot be relied upon. Mr. Trump talked explicitly in interviews about withdrawing military forces from Asia unless Tokyo and Seoul paid more for their presence, and said in March that he was willing to see them build their own nuclear arsenals rather than depend on Washington.

According to one senior administration official, Mr. Kerry told Mr. Obama that a no-first-use pledge would also weaken the nuclear deterrent while Russia is running practice bombing runs over Europe and China is expanding its reach in the South China Sea.

Mr. Obama and his national security team have rejected a second option: “de-alerting” nuclear missiles ready to fire on short notice. The fear is that in a crisis, “re-alerting” the weapons could escalate a conflict.

Earlier, Mr. Obama and his aides also decided against eliminating one element of the “triad” of land-, air- and submarine-launched weapons. The idea was to remove the missiles based in silos across the American West, which are considered outdated and vulnerable to a first strike. But the Pentagon argued strongly that the ground-based missiles were the part of the system with which they had the most assured communications, and that it was too risky to get rid of them.

In the past year, arms control advocates, including some of Mr. Obama’s former aides, have argued that Mr. Obama still has time to repair his reputation as an atomic visionary.

“Let Obama be Obama,” Andrew C. Weber, an assistant secretary of defense for atomic programs from 2009 to 2014, said in an interview.