Alley died of cancer that was only recently discovered, her children True and Lillie Parker said in a post on Twitter. Her manager Donovan Daughtry confirmed the death in an email to The Associated Press.

"As iconic as she was on screen, she was an even more amazing mother and grandmother," Alley's children's statement on Monday said.

She starred opposite Ted Danson as Rebecca Howe on Cheers, the beloved NBC sitcom about a Boston bar, from 1987 to 1993. She joined the show at the height of its popularity after the departure of original star Shelley Long.

Alley would win an Emmy for best lead actress in a comedy series for the role in 1991.

"I only thank God I didn't have to wait as long as Ted," Alley said in her acceptance, gently ribbing co-star Danson, who had finally won an Emmy for his role as Sam Malone in his eighth nomination the previous year.

She would take a second Emmy for best lead actress in a miniseries or television movie in 1993 for playing the title role in the CBS TV movie David's Mother.

She had her own sitcom on the network, Veronica's Closet, from 1997 to 2000.

In the 1989 comedy Look Who's Talking, which gave her a major career boost, she played the mother of a baby whose inner thoughts were voiced by Bruce Willis. She would also appear in a 1990 sequel Look Who's Talking Too, and another in 1993, Look Who's Talking Now.

John Travolta, her co-star in the trilogy, paid tribute in an Instagram post.

"Kirstie was one of the most special relationships I've ever had," Travolta said, along with a photo of Alley.

"I love you Kirstie. I know we will see each other again."

She would play a fictionalised version of herself in the 2005 Showtime series Fat Actress, a show that drew comedy from her public and media treatment over her weight gain and loss.

She dealt with the same subject matter in the 2010 A&E reality series Kirstie Alley's Big Life, which chronicled her attempt to lose weight and launch a weight-loss program while working as a single mother in an unconventional household that included pet lemurs.

Alley said she agreed to do the show in part because of the misinformation about her that had become a tabloid staple.

"Anything bad you can say about me, they say," Alley told the AP at the time.

"I've never collapsed, fainted, passed out. Basically, anything they've said, I never. The only true thing is I got fat."

In recent years she appeared on several other reality shows, including a second-place finish on Dancing With the Stars in 2011. She appeared on the competition series The Masked Singer wearing a baby mammoth costume earlier this year.

She appeared in the Ryan Murphy black comedy series Scream Queens on Fox in 2015 and 2016.

One of her co-stars on the show, Jamie Lee Curtis, said on Instagram Monday that Alley was "a great comic foil" on the show and "a beautiful mama bear in her very real life".

Alley's Cheers co-star Kelsey Grammer said in a statement that "I always believed grief for a public figure is a private matter, but I will say I loved her."

A native of Wichita, Kansas, Alley attended Kansas State University before dropping out and moving to Los Angeles.

Her first television appearances were as a game show contestant, on The Match Game in 1979 and Password in 1980.

She made her film debut in 1982's Star Trek: The Wrath of Khan.

Alley was married to her high school sweetheart from 1970 to 1977, and to actor Parker Stevenson from 1983 until 1997.

She told the AP in 2010 if she married again, "I'd leave the guy within 24 hours because I'm sure he'd tell me not to do something."

Australian Associated Press