WASHINGTON — 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.

The tensions bubbled to the surface this week with the disclosure that the White House had abandoned plans to nominate a prominent Korea expert, Victor D. Cha, as ambassador to South Korea. Mr. Cha suggested that he was sidelined because he warned administration officials against a “preventive” military strike, which, he later wrote, could spiral “into a war that would likely kill tens, if not hundreds, of thousands of Americans.”

But the divisions go back months, officials said. When North Korea tested an intercontinental ballistic missile in July that experts concluded was capable of reaching the West Coast of the United States, the National Security Council convened a conference call that included Secretary of Defense Jim Mattis and Secretary of State Rex W. Tillerson.

After General McMaster left the room, Mr. Mattis and Mr. Tillerson continued to speak, not realizing that other participants were still on the line. The officials familiar with the matter overheard them complaining about a series of meetings that the National Security Council had set up to consider options for North Korea — signs, Mr. Tillerson said, that it was becoming overly aggressive.

For now, the frustration at the White House appears to be limited to senior officials rather than Mr. Trump himself. But the president has shown impatience with his military leaders on other issues, notably the debate over whether to deploy additional American troops to Afghanistan.

As they examine the most effective way of giving credibility to Mr. Trump’s threat of “fire and fury,” officials are considering the feasibility of a preventive strike that could include disabling a missile on the launchpad or destroying North Korea’s entire nuclear infrastructure. American officials are also said to be considering covert means of disabling the nuclear and missile programs.

While General McMaster also favors a diplomatic solution to the impasse, officials said, he emphasizes to colleagues that past efforts to negotiate with North Korea have forced the United States to make unacceptable concessions.

The Pentagon has a different view. Mr. Mattis and the chairman of the Joint Chiefs of Staff, Gen. Joseph F. Dunford Jr., argue forcefully for using diplomacy. They have repeatedly warned, in meetings and on video conference calls, that there are few, if any, military options that would not provoke retaliation from North Korea, according to officials at the Defense Department.

Representatives of Mr. Mattis and General Dunford denied that they have slow-walked options to the White House.

The Pentagon press secretary, Dana W. White, said that Mr. Mattis “regularly provides the president with a…