President Donald Trump interviewed four candidates for the job of national security adviser Sunday, and may meet more on Monday, a White House spokeswoman said.

The vacancy was created after the president’s first adviser, Mike Flynn, resigned under pressure last week.

The potential replacements who visited Mr. Trump’s Mar-a-Lago estate in Florida were Army strategist Lt. Gen. H.R. McMaster, former United Nations Ambassador John Bolton, acting national security adviser Keith Kellogg, and U.S. Military Academy superintendent Lt. Gen. Robert Caslen.

At least two earlier candidates withdrew due to concerns over how much control they would be allowed over staffing and procedures, according to people familiar with the matter.

White House spokeswoman Sarah Sanders denied reports that the new adviser would not have the authority to build a new team in the National Security Council. “Whoever takes this position…in terms of staffing they’ll have full authority to make those decisions,” she said.

Ms. Sanders also defended the firing this past week of an NSC staffer who had reportedly criticized the Trump administration during a private meeting at a Washington think tank. “If you don’t support the president’s agenda it would be very hard to take a position where your job is to carry out and help him accomplish his agenda,” she said.

Ms. Sanders said Saturday that Mr. Trump “may have some additional meetings and names tomorrow,” as he weighs his choice for security adviser. Here’s a more detailed look at the four he met Sunday.

Lt. Gen. H.R. McMaster

A military strategist with extensive battle experience, Gen. McMaster is now director of the Army Capabilities Integration Center at Fort Eustis, Va. Gen. McMaster, 54 years old, is a decorated officer with leadership experience in military operations in both Iraq and Afghanistan. He’s a 1984 graduate of West Point, where he played rugby.

During the 1991 Gulf War, Gen. McMaster gained renown as a captain commanding a tank troop in the Battle of 73 Easting. His Eagle Troop of nine tanks destroyed dozens of Iraqi Republican Guard tanks and vehicles without loss. He was awarded the Silver Star, and the battle is featured in several books about Operation Desert Storm, including Tom Clancy’s “Armored Cav.”

While a colonel during the second Iraq war, he became a counterinsurgency expert and senior adviser to Gen. David Petraeus, commander of U.S. forces in Iraq and later director of the Central Intelligence Agency. Gen. Petraeus had himself been a candidate for the White House security adviser job before withdrawing his name last week.

Known as a vocal critic of the status quo in the military, Gen. McMaster was twice turned down for promotion before becoming a brigadier general in 2008. His 1997 book, “Dereliction of Duty,” was critical of the Joint Chiefs of Staff and then-Defense Secretary Robert McNamara for their handling of the Vietnam War.

Time magazine named Gen. McMaster to its 2014 list of the 100 most influential people in the world, describing him as “the architect of the future U.S. Army.”

Lt. Gen. Robert Caslen

Gen. Caslen, 63 years old, spent his entire career in the Army, including key leadership roles in Iraq and Afghanistan. He graduated from the U.S. Military Academy at West Point in 1975, where he was the football team’s starting center for two years. He returned as school superintendent in July 2013.

He had previously been chief of the Office of Security Cooperation in Iraq. He also commanded U.S. forces in northern Iraq during President Barack Obama’s first term, at a time when the Obama administration was debating withdrawing troops from Iraq.

In 2005, Gen. Caslen, along with six other generals and military officers, appeared in a controversial video promoting Christian Embassy, a nonprofit evangelical organization. The Pentagon’s inspector general found that Gen. Caslen and the other participants had acted improperly, and that participation in uniform appeared to show the military endorsed the group’s views.

In a 2015 interview with the New York Observer, Gen. Caslen said he was troubled by the rise of Islamic State in Iraq but didn’t feel that U.S. soldiers died in vain during the Iraq war.

“I’m in support of what’s going on over there and the work that they’re doing and I have some hope that it’ll end up with the right solution,” he said.

John Bolton

The security adviser role isn’t the first vacancy to cause Mr. Trump to look to John Bolton, 68. He was previously considered as a possible secretary of state, and then to be the No. 2 official in the State Department.

Mr. Bolton is a senior fellow at the conservative American Enterprise Institute and a frequent commentator on Fox News.

He cultivated a reputation as a brash conservative with an aggressive style while chief arms control official at the State Department, and as U.S. ambassador to the United Nations under President George W. Bush.

Mr. Bolton took tough stances on how to address nuclear programs in North Korea and Iran, advocating against diplomacy while the countries’ hard-line governments were in power. He also pushed for limiting U.S. involvement in multilateral institutions and treaties, including the International Criminal Court, the Antiballistic Missile Treaty and the Kyoto Protocol.

Mr. Bolton left his U.N. post after he failed to gain enough support in Congress to be confirmed in 2006. President Bush had originally used a recess appointment to put him in the role after his nomination had been blocked by a Democratic filibuster. His initial nomination faced opposition from Democrats, and some Republicans, over allegations that he tried to spin intelligence to support his political views, and that he harassed subordinates who didn’t share his views.

The White House security job does not require Senate confirmation, which would make it an easier slot for Mr. Bolton to fill than the two positions at the State Department. Even some Republican lawmakers suggested they would oppose his nomination to those jobs.

“The problem with John Bolton is he disagrees with President Trump’s foreign policy,“ Sen. Rand Paul (R., Ky.) said Sunday on ABC’s “This Week.” ”John Bolton still believes the Iraq war was a good idea. He still believes that regime change is a good idea. He still believes that nation-building is a good idea. »

Keith Kellogg

Joseph Keith Kellogg Jr., 72 years old, is a retired three-star general in the U.S. Army, who has this past week been acting national security adviser following Mr. Flynn’s departure.

He served in the 101st Airborne in Vietnam, and was later a special forces adviser to the Cambodian Army.

Mr. Kellogg commanded the 82d Airborne Division beginning in 1996, and became chief operating officer for the transition government of Iraq after the 2003 war. After retiring from the military, he became an adviser to Oracle Corp.

Mr. Kellogg joined the Trump campaign as a foreign-policy adviser in March 2016 and, following the election, was named NSC chief of staff under Mr. Flynn.