A Colorado man, carrying an overnight bag and intermingling with members of the U.S. Marine Orchestra, slipped into the White House on inauguration Sunday and wandered about for 15 minutes before he was arrested by red-faced Secret Service agents, the White House said yesterday.

Despite extraordinary security precautions, Robert Latta, a 45-year-old water meter reader from Denver, walked into the White House and took his own private tour while waiting for the Jan. 20 noon swearing-in ceremonies to begin, the Secret Service said.

"He found the run in the White House stocking," said Anthony Tansimore, appointments secretary to Rep. Patricia Schroeder (D-Colo.). Her office heard about Latta's unauthorized visit, subsequent arrest and six-day jailing when he dropped by Monday to ask for help in getting his driver's license back.

"It was a breach of security," Secret Service spokesman Jack Taylor said yesterday. "We're doing an internal evaluation."

The Reagans were attending church at the time of the incident.

Latta was arrested shortly before 10:30 a.m. and never got to watch President Reagan take the official oath of office for his second term. But he did wander into the room where the ceremony was scheduled to take place, according to Taylor.

Although initial news accounts reported that Latta was found sitting at the Reagans' dining table in the private family quarters on the second floor, both the White House and the Secret Service adamantly denied at a press briefing yesterday that the intruder entered the first family's quarters.

The subject of what was being called the "White House visitor" occupied most of yesterday's regular press briefing at the White House, which was attended by a Secret Service official.

White House spokesman Larry Speakes, while expressing concern about the intrusion, called it one of "a number of incidents" that occur "virtually on a daily basis." He said "threats, attempts, phone calls, letters" come into the White House each day and that, on a weekly basis, some individual attempts to enter the White House grounds.

He also disclosed to a surprised White House press corps that a man carrying a handgun had "filtered into" an area where a group of reporters was covering a scheduled speech by Reagan in Alaska last May 1.

The man, carrying a .22-caliber handgun, was taken into custody before the president arrived but was not charged with possessing a weapon because having a handgun is not a violation of law in Alaska.

Speakes, according to a transcript of the press briefing, said he was informed of Latta's arrest the day it happened but did not report the incident to reporters.

The president, he said, was told of the intrusion but wasn't given a full briefing until yesterday.

"Procedural" changes have since been instituted in White House security arrangements but Speakes would not specify the actions taken. Other officials, however, said that security procedures will henceforth include a "head count" so that the Secret Service can better monitor large groups of expected visitors.

The Secret Service has spent a small fortune installing metal detectors, concrete barricades, even missiles on the White House roof -- all to ensure the president's safety. Most reporters and other regular visitors are screened each time they enter the mansion.

But the 33-member orchestra, which visits often, has a top-secret security clearance, Speakes said, and individual members were not checked off by name at the gate.

Latta was charged with unlawful entry, a misdemeanor, on Jan. 20. At an arraignment Jan. 21 at D.C. Superior Court, Latta was ordered sent to St. Elizabeths Hospital for psychiatric evaluation. But U.S. Attorney Joseph E. diGenova said yesterday that, in an apparent court mixup, Latta was never sent to the hospital but was kept at the D.C. Detention Center. He was released from there Friday on $1,000 bond.

Latta, who returned to Denver late Monday, could not be reached for comment. A spokesman for the Denver water department, where he has worked since 1978, said Latta isn't due back from vacation until next week.

But in an interview with the Associated Press, Latta said he "just wanted to see the ceremony" and followed the orchestra into the White House without really thinking he was doing anything wrong.

"I just walked in with the band. I just had my hat and coat on," he said.

He called his incarceration "a little unjustified" but said he had decided on reflection that his White House wanderings might have been unwise.

"Not going through the metal detector or anything . . . somebody could have pinned something on me, maybe a bomb or something, and I might have been in there, why, it might have been bad," he said.

Latta, twice divorced and the father of two, said he had flown to Washington to see the inauguration because "I'm kind of patriotic." He said he had taken a White House tour four days earlier and that he and several others had wandered off from the rest of the group.

"So, you know, I from this didn't see that that'd be such a bad thing, to walk in," Latta said.

It was not clear yesterday whether Latta would return to Washington for his March 5 court date. DiGenova said legal authorities cannot seek to extradite him for a misdemeanor offense.

There were somewhat conflicting accounts at the press briefing about how long Latta was in the White House and where he wandered before he was noticed. There was also more than a little humor in describing what happened.

Speakes said Latta mingled with the orchestra, which had come to the White House to play for the swearing-in ceremonies, and walked in with the musicians when they entered the White House through the East Gate. The musicians were carrying their instruments; Latta was carrying a small bag containing a book and some clothes.

The orchestra members, according to Speakes, were in uniform but wearing overcoats because of the subfreezing weather that day. The musicians were not in any special formation and did not march onto the White House grounds, which, Speakes said, was one reason for the problem.

"Had he been out of step, they would have caught him earlier," Speakes assured reporters.

The group, once cleared at the gate, proceeded to the State Floor of the mansion and prepared for a performance in Cross Hall, a large, formal hall that connects the East Room and the State Dining Room.

Speakes said the chief usher at the White House was the first to observe that Latta, dressed in a suit and tie, did not look like a member of the orchestra. They had taken off their coats by then. "That's what gave them the clue," Speakes said.

A quick check with the Marine officer in charge of the orchestra confirmed that Latta was not a musician, Speakes said, though the Marine officer apparently told White House officials that he "assumed" that Latta was a staff member -- of either the White House or the orchestra, Speakes said he wasn't sure.

At some one point, Latta was seen in the Family Dining Room off on the State Floor, which is occasionally used by the Reagans but which is not part of their private family quarters. The Denver man, whom Speakes said never actually told anyone he was an orchestra member, was subsequently arrested back in the Cross Hall, according to Speakes.

Latta's visit is not the first time an unauthorized person has penetrated White House security. Nuclear protesters and others have frequently gotten inside the gates of the compound, and during the Carter administration, a reporter from a Soviet Union news service agency mistakenly walked into the Oval Office.

Upon discovering Latta, the Secret Service searched with dogs the area where he was believed to have wandered.

A spokesman for the Marine Orchestra said the group had no comment.

"I think all parties agree that there was a mistake made," Speakes said.

Latta stopped by Schroeder's office in Washington on Monday before returning to Denver. He complained about jail conditions and asked for help in getting back his driver's license. He had visited his congresswoman once before, when he got to town to see the inauguration.

"He said he was on vacation," recalled Schroeder aide Tansimore. "He asked if we could suggest some interesting places to see -- one of them being the White House."