Actor Rock Hudson, whose announcement that he was suffering from acquired immune deficiency syndrome (AIDS) galvanized worldwide support to combat the deadly disease, died at his Los Angeles home yesterday at the age of 59.

Hudson's personal physician, Dr. Rexford Kennamer, was called to the actor's home early yesterday by a member of Hudson's household staff. Kennamer pronounced Hudson dead at 9 a.m. Pacific time, according to Hudson's publicist, Dale Olson.

Kennamer would not comment on the exact cause of Hudson's death, attributing it only to "complications" from AIDS, according to a source. "He had extensive Kaposi's sarcoma a form of skin cancer common to AIDS victims ," said a doctor familiar with Hudson's case. "And I know he had severe liver disease."

There were numerous statements of sympathy and praise yesterday from the Hollywood community for Hudson, one of their most well-regarded colleagues. The White House released a statement from President Reagan, who had spoken by phone two months ago with his former colleague when Hudson was hospitalized:

"Nancy and I are saddened by the news of Rock Hudson's death. He will always be remembered for his dynamic impact on the film industry and fans all over the world will certainly mourn his loss. He will be remembered for his humanity, his sympathetic spirit and well-deserved reputation for kindness."

A major screen and television presence for more than 30 years, Hudson had returned to his home in Malibu Aug. 24 after treatment at the UCLA medical center. Earlier this summer, he had flown to France for experimental treatment at the Pasteur Institute in Paris, where it was disclosed he had been suffering from AIDS. The illness, which destroys the body's immune system, had struck 13,611 men and women in the United States as of Oct. 1, according to the national Centers for Disease Control in Atlanta. Of those, 6,944 have died.

The overwhelming majority of its victims have been homosexual men. Hudson's homosexuality, his friends reported on learning he had AIDS, was one of Hollywood's more open secrets.

"I had no idea this was so imminent," said Olson. "I saw him the day before yesterday. He smiled. He was pleasant. He was ill but he was responding."

Hudson's death comes just a little over two months since an item in the entertainment industry trade paper Variety triggered Hollywood rumors and then the Paris announcement that the actor had been suffering from AIDS for more than a year.

That disclosure catapulted AIDS into the public limelight in unprecedented fashion and galvanized the gay community, which had long provided the bulk of what financial and moral support AIDS victims received. AIDS and Rock Hudson became the topic of national magazines and television news shows and the centerpiece of fundraisers across the country.

"That one act probably did more than anything to date in terms of focusing attention on AIDS and the need for support as well as the urgency," said William Misenhimer, the executive director of the new American Foundation for AIDS Research, about Hudson's disclosure. "We're really looking at a health emergency. I don't think people believed that until now."

"The fact that he came out publicly as an AIDS victim means that he has drawn attention to this disease and to the plight of the closeted gay actor and through that his contributions will be everlasting," said one Hollywood gay actor who is on the board of the Alliance for Gay and Lesbian Artists in the entertainment industry.

In Hollywood, the reaction to Hudson's illness was strong and paradoxical. The community rallied behind one of their own who had been afflicted with this fatal disease and raised over a million dollars for AIDS research and support at a lavish black-tie benefit several weeks ago. At the same time, the vagueness over how AIDS is spread raised paranoia and homophobia in the entertainment industry, where intimate kissing scenes are often part of the daily work. And throughout the country, fear over getting the disease escalated.

Yesterday, however, there was nothing but an outpouring of affection and sorrow for Hudson from his Hollywood colleagues.

"I love him and he is tragically gone," said actress Elizabeth Taylor, a Hudson friend who was also an early supporter of AIDS causes. "Please God, he has not died in vain."

A tearful Doris Day, a costar with Hudson in a number of romantic comedies including the popular "Pillow Talk," told United Press International, "Oh, my God, what can I say? . . . Life is eternal. I hope we will meet again." Hudson's last public appearance was with Day to promote a new cable television show of hers. Those pictures of a smiling but gaunt and sickly looking Hudson stunned the public only a couple of weeks before he revealed his illness.

Susan Saint James, Hudson's costar on the popular television show of the 1970s, "McMillan and Wife," released a statement yesterday saying, "No one taught me more than Rock did about the values of humanity and professionalism in show business and in life. I loved him so much."

The producers and cast of "Dynasty," the television series that Hudson worked on last season, released numerous statements of condolences.

The "Dynasty" cast, particularly actress Linda Evans, with whom Hudson did romantic scenes, was rumored to be concerned about being exposed to the AIDS virus and was dogged by press inquiries over those worries, all of which were denied repeatedly.

Linda Evans said, " . . . I feel his greatest gift to the world was in his acknowledgment of his disease and in his willingness to educate people and raise their consciousness. His death is a great loss to all of us, but his legacy will be our continued fight for a cure for AIDS."

Hudson spent his recent days "visiting with friends, reading, watching television -- lots of old movies -- just sort of playing with the dogs and wandering around in the garden," according to Olson. Hudson's visitors included Taylor, Roddy McDowall, actress Nancy Walker, Robert Wagner and actor Jack Scalia.

He was working almost every day that he felt up to it with writer Sara Davidson on a book that will undoubtedly reveal many of the details of his life.

Hudson, who made his career as a suave, sophisticated leading man, toiled away in small, undistinguished film parts in the late '40s and early '50s that nonetheless built for him a following of fans. His first major role, in 1954, was opposite Jane Wyman in the remake of "Magnificent Obsession." The $5 million box office made him Universal's top romantic leading man. In 1956, he starred with Taylor and James Dean in "Giant," winning an Oscar nomination and critical praise. In the late '50s and '60s, he switched to frothy sex comedies with such actresses as Day and Gina Lollobrigida and became even more popular. In the '70s, he made the transition to television with the successful "McMillan and Wife."

Hudson's brief studio-arranged marriage in the 1950s to Phyllis Gates, his agent's secretary, ended in divorce after three years. It is unclear if any friend was with Hudson at the time of his death, though one longtime friend and associate, a Los Angeles publicist named Tom Clark, was at his home immediately afterward.

According to Olson, Clark had no comment, and said only "I don't want to talk to anyone."

Olson said Hudson's representatives had asked that instead of sending flowers, people donate to the American Foundation for AIDS Research, 9601 Wilshire Blvd., Beverly Hills, Calif. 90212. The foundation encompasses the Rock Hudson AIDS Foundation, which was recently started. The actor had donated $250,000 of his own funds to it.

Funeral arrangements had not been announced last night