By Peter and Maggie Haberman, New York Times–

President Trump will interview four candidates on Sunday to replace his dismissed national security adviser, three of them military veterans, but one of America’s most prominent retired generals, whose name had been floated, is not in the running.

A White House spokesman said on Saturday that Mr. Trump would speak with Lt. Gen. H. R. McMaster, a prominent military strategist; Lt. Gen. Robert L. Caslen Jr., the superintendent of the United States Military Academy at West Point; and Keith Kellogg, a retired lieutenant general already serving as acting national security adviser.

Mr. Trump, who is spending the weekend in Florida, will also interview John R. Bolton, who served as President George W. Bush’s ambassador to the United Nations and has previously been considered for deputy secretary of state. Sean Spicer, the White House press secretary, told reporters that “potentially others” might also be considered but that David H. Petraeus, the retired general and former C.I.A. director, was not a candidate.

The national security adviser is a crucial figure in any White House, but Mr. Trump has struggled to find the right person to fill the post. His first national security adviser, Michael T. Flynn, a retired lieutenant general, lasted only 24 days before Mr. Trump requested his resignation for misinforming Vice President Mike Pence about the nature of a conversation with Russia’s ambassador to the United States.

The list of candidates now being considered reflects Mr. Trump’s continued interest in bringing top military officers into his administration. Other generals have served as national security adviser — notably Brent Scowcroft and Colin L. Powell — but the president seems reluctant to cast a net much wider than the officer corps.

At a news conference on Thursday, Mr. Trump said he was comfortable dismissing Mr. Flynn in part because he had “somebody that I think will be outstanding for the position.” He seemed to be referring to Robert S. Harward, a retired vice admiral and Navy SEAL, but Mr. Harward later turned down the job.

The search for a new adviser has been complicated by uncertainty in the foreign policy world about the role of Stephen K. Bannon, the president’s chief strategist, who has been given a seat on a cabinet-level National Security Council committee. Mr. Harward was said to have expressed concern about how much autonomy he would have had. Mr. Petraeus was said to have similar concerns, although some close to Mr. Trump said he was never a serious candidate.


John R. Bolton in 2011. Mr. Bolton served as President George W. Bush’s ambassador to the United Nations.CreditSteve Hebert for The New York Times

A White House official, who like others insisted on anonymity to discuss the search more candidly, rejected reports that Mr. Harward had been concerned about a lack of autonomy in the role, insisting that he had been promised full personnel and structuring authority to clean house. Mr. Bannon was Mr. Harward’s biggest supporter in the West Wing for the national security adviser role, whisking him into a secret meeting with the president on Monday.

On Saturday evening, a senior administration official described General McMaster and General Caslen as the leading candidates.

The one candidate who has not emerged from the military is Mr. Bolton, an outspoken conservative respected by Mr. Bannon, although it is unclear if Mr. Bannon is supporting him for the national security job. Mr. Bolton does have support from two important donors to Mr. Trump, according to people briefed on the White House process: the casino magnate Sheldon G. Adelson and the philanthropist Rebekah Mercer.

Mr. Bolton shares Mr. Trump’s strong antipathy toward the Iran nuclear deal negotiated by former President Barack Obama, and he would presumably continue the tough approach begun by Mr. Flynn of pressuring Tehran over its ballistic missile program and its sponsorship of terrorist groups. But Mr. Bolton has also taken a stronger position on Russia than Mr. Trump or Mr. Flynn. In a recent op-ed article in The Wall Street Journal, he seemed to try to reconcile that by agreeing with Mr. Trump’s criticism of Mr. Obama’s New Start arms control treaty with Russia.

Mr. Bolton is a favorite of conservatives but an adversary of Democrats, who blocked him for confirmation as ambassador to the United Nations. Mr. Bush used his recess appointment power to install him anyway, but came to regret it when Mr. Bolton, after leaving office, became a harsh critic for what he said was the president’s unwise willingness to negotiate with North Korea.

General McMaster, a highly decorated Army officer, is considered one of the military’s leading intellectuals. He earned something of a cult status in the military as a young major for his influential 1997 book, “Dereliction of Duty,” an indictment of the military’s failure to stand up to Lyndon B. Johnson and other civilian leaders during the Vietnam War.

But General McMaster has also proved himself in the field, leading a successful counterinsurgency effort in 2005 to secure Tal Afar in northern Iraq. He was critical of the way the Bush administration went to war in Iraq and became an important thinker behind the strategy change that helped turn the war around. Foreign Policy magazine called him “the brain behind Petraeus.” General McMaster is now the director of the Army Capabilities Integration Center at Fort Eustis in Virginia.

General Caslen, who was in the Pentagon on Sept. 11, 2001, and went back into the building after it was hit, served in key roles in Iraq and Afghanistan. He was commander of the 25th Infantry Division (Light) and commander of coalition forces in northern Iraq. A West Point graduate, he took command of the military academy in 2013. Mr. Bannon is a former naval officer, and his daughter graduated from West Point.

Mr. Kellogg served for 36 years in the Army, including two tours in Vietnam, where he earned the Silver Star and other medals. He commanded the 82nd Airborne Division and was chief operating officer of the Coalition Provisional Authority in Iraq before retiring in 2003. He advised Mr. Trump on foreign policy during his campaign and was named chief of staff at the National Security Council.

Correction: February 18, 2017
An earlier version of this article misstated Stephen K. Bannon’s military background. He is a former naval officer; he did not graduate from West Point. (His daughter graduated from West Point.)