Her family announced the death in a statement but did not cite a cause.

“Murder, She Wrote” — with its opening montage of Ms. Lansbury pecking at a typewriter and facing down danger in a coastal Maine town — was one of the most popular TV shows of the 1980s and 1990s. To tens of millions of viewers, the veteran actress with a trace of a British accent personified Jessica Fletcher, the widow-turned-detective whose genteel manner masked her wits.

To a younger generation, Ms. Lansbury was best remembered as the voice of Mrs. Potts, the tenderhearted teapot who sings the Oscar-winning title song in the animated Disney feature “Beauty and the Beast” (1991).

Such cherished performances may have suggested that Ms. Lansbury was a specialist in plucky, non-threatening roles. Yet over seven decades in show business, she had two earlier and distinct phases of her career — on-screen and then on Broadway — in which she revealed herself as an artist of immense range and power.

“Hardly anyone can match her career for success, longevity and variety,” said film scholar Jeanine Basinger.

In her teens, Ms. Lansbury earned Oscar nominations for supporting roles in her first two movie appearances: as an impudent and seductive Cockney maid in “Gaslight” (1944) and as a sweetly innocent music-hall singer in “The Picture of Dorian Gray” (1945). In the latter, her high and light voice was used to poignant effect in the ditty “Goodbye, Little Yellow Bird,” forecasting her own doom.

Ms. Lansbury had photogenic features: peaches-and-cream skin, blue eyes and a blond mane. To her dismay, she never made the leap into leading roles, in part because she lacked the ethereal and glamorous presence of a 1940s star.

She could act years, even decades, beyond her age and settled into a long run of scolding and ruthless character roles opposite much-older leading men such as Walter Pidgeon (“If Winter Comes” in 1947) and Spencer Tracy (“State of the Union” in 1948).

Later, Ms. Lansbury was the movie mother to performers marginally her junior: Elvis Presley in “Blue Hawaii” (1961), Warren Beatty in “All Fall Down” (1962) and Laurence Harvey in “The Manchurian Candidate” (1962). Presley, she later said, “used to send me Mother’s Day cards.”

In “The Manchurian Candidate,” based on Richard Condon’s novel about Cold War paranoia, she played a domineering political wife and mother who helps carry out a communist plot to take over the White House, in part by manipulating her son into serving as an assassin.

“Lansbury creates a modern-age Lady Macbeth with the skill of a sorceress,” critic Peter Travers wrote in People magazine upon the film’s 1988 rerelease. “It’s an astonishing, engulfing performance.”

The film, also starring Frank Sinatra, is now regarded as a taut classic. But on its initial release, it flopped at the box office and did little to advance Ms. Lansbury’s career, despite having brought the actress her third and final Oscar nomination.

“Everyone kept telling me, ‘You’re a shoo-in,’ and I sat there with my speech prepared,” she told her biographer, Martin Gottfried. When Patty Duke won for playing Helen Keller in “The Miracle Worker,” Ms. Lansbury continued, “it was like your stomach has fallen out of your body. It bothered me desperately.”

Tired of playing unsympathetic or over-the-hill women — “I’ve played so many old hags most people think I’m 65 years old,” she quipped at 41 — she turned to theater work.

On Broadway, Ms. Lansbury received six Tony Awards, including four for best actress in a musical and one for lifetime achievement. Her first win recognized her performance as a bohemian socialite caring for her orphaned nephew in Jerry Herman’s musical comedy “Mame” (1966). The show brimmed with chorus boys and flamboyant costumes and provided Ms. Lansbury with the showstopper “It’s Today.”

In Stephen Sondheim’s “Sweeney Todd” (1979), a brooding and dissonant “musical thriller,” Ms. Lansbury garnered a Tony as a London piebaker who becomes an accessory to murder and cannibalism.

Stephen Sondheim, central figure in American musical theater, dies at 91

She collected a Tony for her starring role in the 1969 Herman musical and anti-capitalist satire “Dear World.” As the forceful stage mother Mama Rose, she won again for “Gypsy,” a 1974 revival of the Sondheim-Jule Styne-Arthur Laurents musical that allowed her to reinvent with nuance and subtlety a part that had all-but-been defined for years by the Broadway belter Ethel Merman.

Ms. Lansbury’s final competitive win — for best featured actress in a play — was for “Blithe Spirit,” a 2009 revival of the Noel Coward comedy in which she played a dotty clairvoyant.

For all her film and stage work, it was on television that Ms. Lansbury, nearing 60, became a household name with “Murder, She Wrote” on CBS. Her character was canny but understated, upbeat but not Pollyannaish, bemused but not cynical.

“She embraced the concept of being a middle-aged woman who was a widow and lived in a small town,” Basinger said, noting the show’s range from scary to funny to sentimental. “She didn’t try to glamorize it or deviate from it. The show would not have been a success with anyone else.”

The Jessica Fletcher role, initially turned down by “All in the Family” star Jean Stapleton, brought Ms. Lansbury 12 Emmy nominations. “Murder, She Wrote” drew mostly older viewers who tuned in to see long-ago movie stars such as June Allyson, Kathryn Grayson and Hurd Hatfield as murder suspects in the weekly plot lines. Ms. Lansbury had known many of the actors from her formative years at Metro-Goldwyn-Mayer — only this time she was the headliner.

After 11 seasons, ratings plummeted when, in an attempt to draw younger viewers, CBS moved the program from its longtime Sunday night spot to Thursdays. Forced to compete with shows like “Friends” on NBC, “Murder, She Wrote” was canceled.

“It was really a fluke success and came at a time when that kind of family entertainment seemed needed,” Ms. Lansbury told the New York Times. “The character was very calming.”

Angela Brigid Lansbury was born in London on Oct. 16, 1925. Her paternal grandfather, George Lansbury, became leader of England’s Labour Party in the 1930s. Her father, Edgar, was a businessman, and her mother was a stage and film actress known as Moyna Macgill.

Her parents divorced, and Angela was 9 when her stepfather died from cancer. Movies became a refuge, she said. Her mother made sure she and her three siblings had piano and dance lessons.

Fleeing the German blitz during World War II, the family came to New York in 1940 and later settled in Los Angeles, where Macgill used her contacts among Britons in the film colony to find acting work for herself and Angela. At 17, Ms. Lansbury won a screen test at MGM, which led to roles in “Gaslight” and “The Picture of Dorian Gray.”

Continuing in supporting parts, she played the older sister to Elizabeth Taylor in “National Velvet” (1944) and to Hedy Lamarr’s Delilah in Cecil B. DeMille’s biblical epic “Samson and Delilah” (1949). She also was a saloon dance-hall queen in the musical “The Harvey Girls” (1946), starring Judy Garland.

Studio executives declined to give Ms. Lansbury leading roles she coveted, such as the wily Lady de Winter in “The Three Musketeers” (1948), a role that went to Lana Turner. Ms. Lansbury played the queen of France.

“I had the ability but I didn’t have the name,” she remarked. “I was all talent and no looks.”

Sensing a downward career trajectory, Ms. Lansbury eventually negotiated a release from her MGM contract. As a freelancer, she played a princess in the Danny Kaye comedy “The Court Jester” (1954), Orson Welles’s blowzy lover in “The Long, Hot Summer” (1958) and a series of overbearing mother and wife roles in the 1960s.

Ms. Lansbury grew so tired of unpleasant or sinister parts that she turned down director Milos Forman’s offer to play Nurse Ratched in “One Flew Over the Cuckoo’s Nest” (1975), a role for which Louise Fletcher won the Oscar for best actress.

For the rest of her screen career, Ms. Lansbury vowed to play likable characters, from the apprentice witch in Disney’s “Bedknobs and Broomsticks” (1971) to a society matron in the Jim Carrey comedy “Mr. Popper’s Penguins” (2011).

Broadway fully showcased the sweep of her abilities. She proved a deft farceuse in “Hotel Paradiso” (1957), featuring the comic great Bert Lahr, and played a vulgar mother in “A Taste of Honey” (1960), a drama with Joan Plowright as her pregnant and abandoned daughter.

Ms. Lansbury’s musical theater debut came in “Anyone Can Whistle” (1964), a Laurents and Sondheim musical in which she was the imperious mayor of a seedy town. Critics loathed the show — finding its absurdist satire and nonconformist theme too clever by half — and it ran only nine performances.

But one ticket-buyer, composer Jerry Herman, loved it and became Ms. Lansbury’s champion for his show “Mame.” She spent two years in the role, which transformed her into a theatrical star.

A series of demanding musicals, especially “Sweeney Todd” opposite Len Cariou in the title role, cemented her reputation as a consummate professional, able to conjure a bonkers music-hall spirit with tunes such as “The Worst Pies in London” and “By the Sea.”

Ms. Lansbury’s accolades included the National Medal of Arts in 1997 and the Kennedy Center Honors in 2000. In 2013, she received an honorary Oscar and was made a Dame of the British Empire by Queen Elizabeth II.

In addition to the struggles of her career, Ms. Lansbury spoke openly about complications in her personal life. She had a brief early marriage to actor Richard Cromwell, who she said was gay. In 1949, she wed Peter Shaw, who became a top talent agent. She said their two children, Deirdre and Anthony, developed drug problems, leading the family to leave their home in Malibu, Calif., and spend much of the 1970s in County Cork, Ireland, to stay at a remove from what she said was the negative influence of Hollywood.

Shaw died in 2003. In addition to her two children, survivors include a stepson, David Shaw; a brother; three grandchildren; and five great-grandchildren.

In interviews, Ms. Lansbury played down her hard-charging ambition and said she considered herself a “journeyman actor” who had gotten lucky.

“I just did what was handed to me but the things that were handed to me were quite extraordinary,” she told the Sunday Express in 2014. “I have an inordinate amount of energy, and I’ve got to expend it somehow. I always say there are two things in life that I know how to do — one is to keep house and the other one is to act.

“And acting usually takes precedence, so the place is a bit messy at times.”