LOS ANGELES, Dec. 14— George Montgomery, a Westerner to the core, who went from prizefighter to stuntman to cowboy star before turning his energies to sculpture, furniture-making and painting, died on Tuesday at his home in Rancho Mirage, Calif. He was 84.

The rugged, soft-spoken actor was also well known as half of one of Hollywood's most visible couples in the 1940's and 50's, when he was married to the singer Dinah Shore.

After making dozens of B westerns in the 30's and early 40's, often appearing under his actual name, George Letz, Mr. Montgomery was signed by 20th Century Fox, which planned to turn him into a major star. It was then that he began to use Montgomery, his real middle name. At Fox, he appeared with Betty Grable in ''Coney Island'' (1943), Ginger Rogers in ''Roxie Hart'' (1942), Gene Tierney in ''China Girl'' (1942), Maureen O'Hara in ''10 Gentlemen From West Point'' (1942) and even in a musical, ''Three Little Girls in Blue'' (1946), opposite June Haver.

While Mr. Montgomery drew praise for his straightforward performance as detective Philip Marlowe in ''The Brasher Doubloon'' (1947), based on Raymond Chandler's ''High Window,'' he was never really able to break free from the public's view of him as a cowboy star. And it was to the saddle that he returned in the 1950's and 60's in more than three dozen roles whose titles tell the story, from ''Dakota Lil'' (1950) to ''Masterson of Kansas'' in 1954 to ''Toughest Gun in Tombstone'' in 1958.

Perhaps it is telling that once Mr. Montgomery began producing and directing his own films in the 1960's, he never once cast himself as a cowboy. Instead, he enjoyed setting the films, often World War II adventures, in exotic locations in Africa and Asia.

One of Mr. Montgomery's bronze sculptures showed Ronald Reagan on horseback. He had been a close friend of the former president for decades, and Nancy Reagan issued a statement on Wednesday on the couple's behalf. ''Ronnie and I have known him for so many years that it will be hard to imagine him gone,'' she said.

George Montgomery Letz was born in 1916 and raised on a remote Montana ranch. He boxed as a heavyweight for a short while before enrolling at the University of Montana, where he was active in school athletics and majored in interior design. He left college after one year and eventually made his way to Hollywood where he was quickly hired in 1935, appearing as a stuntman or extra in dozens of westerns starring Gene Autry and others, beginning with ''The Singing Vagabond.'' His largest role of the period was as one of five men suspected by townspeople of being the mysterious masked gunman in ''The Lone Ranger'' serial of 1938.

After signing with Fox in 1940, Mr. Montgomery was initially put into some of the studio's B westerns, most notably ''The Cisco Kid and the Lady'' in 1940 and ''Riders of the Purple Sage'' in 1941. But later in 1941, beginning with ''Cadet Girl,'' Mr. Montgomery shifted away from westerns and toward more high-profile projects opposite some of the studio's biggest leading ladies. (That same year he was briefly engaged to Hedy Lamarr.)

Dinah Shore, one of the period's top singing stars, told interviewers that she fell in love with Mr. Montgomery when she saw him on the screen in ''The Cowboy and the Blonde'' in 1941. They were married in 1943, the same year Mr. Montgomery joined the Army Air Force, where he served until 1946. Like many actors who served in the military during World War II, Mr. Montgomery returned to find that new faces had emerged to take the top roles in many films, and that he was not being offered the same kind of high-level projects that he drew before the war.

But he still had a few successes, particularly ''The Brasher Doubloon,'' after which some critics compared his Marlowe favorably with Humphrey Bogart's in Howard Hawks's ''Big Sleep,'' which was released the same year.

Shore and Mr. Montgomery had two children; a daughter, now Melissa Ann Hime, and a son, John David Montgomery. The actor is also survived by three grandchildren.

The couple separated in 1961 and were divorced two years later. Also in 1963, Mr. Montgomery was involved in a bizarre incident in which his housemaid apparently tried to shoot him. A note found in the woman's pocket said that she disapproved of the way the actor spent time with ''stupid looking glamour girls,'' so she intended to shoot him and then kill herself. She failed at both.

By the late 50's, Mr. Montgomery was also appearing in many television series -- usually westerns -- and even took a regular role for two years in a series called ''Cimarron City.'' He also appeared on ''Bonanza,'' ''Wagon Train,'' ''Hawaiian Eye,'' ''I Spy'' and other series.

During this period, though, his interest was shifting toward woodworking. He built 11 homes and made highly praised, handmade wooden furniture for himself, for friends and for wealthy clients. In the 70's he turned to sculpture, and his most ambitious work was a bronze recreation of Custer's Last Stand that took him more than a year to complete. He also enjoyed making bronzes of his movie star friends on horseback, including Mr. Reagan and John Wayne. He was also a serious collector of Western art.

In 1981 he published ''The Years of George Montgomery,'' in which he discussed and displayed his work, both as a filmmaker and an artist.

Mr. Montgomery's paintings and sculpture have been displayed in museums and galleries in Seattle and Palm Springs and at the Autry Museum of Western Heritage in Los Angeles.

Photo: George Montgomery in ''The Texas Rangers'' (1951).