The White House has grown frustrated in recent weeks by what it considers the Pentagon’s reluctance to provide President Trump with options for a military strike against North Korea, according to officials, the latest sign of a deepening split in the administration over how to confront the nuclear-armed regime of Kim Jong-un.

The national security adviser, Lt. Gen. H. R. McMaster, believes that for Mr. Trump’s warnings to North Korea to be credible, the United States must have well-developed military plans, according to those officials.

But the Pentagon, they say, is worried that the White House is moving too hastily toward military action on the Korean Peninsula that could escalate catastrophically. Giving the president too many options, the officials said, could increase the odds that he will act.