American film and TV actress Kirstie Alley has died after a secret short battle with cancer.

Alley, the star of 1980s sitcom Cheers and the Look Who’s Talking films, along with a string over other TV and film hits, was 71.

Her children, True and Lillie Parker, confirmed Alley’s death in a statement on Tuesday afternoon Australian time.

“We are sad to inform you that our incredible, fierce and loving mother has passed away after a battle with cancer, only recently discovered,” they said in a statement.

“She was surrounded by her closest family and fought with great strength, leaving us with a certainty of her never-ending joy of living and whatever adventures lie ahead.

“As iconic as she was on screen, she was an even more amazing mother and grandmother.”

Alley’s son and daughter also thanked the “incredible team of doctors and nurses” at Florida’s Moffitt Cancer Centre.

Alley’s manager Donovan Daughtry also confirmed the death in an email to The Associated Press.

Alley 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 won an Emmy for best lead actress in a comedy series for the role in 1991. She got a second 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 film Look Who’s Talking, which gave her a major career boost, Alley played the mother of a baby whose inner thoughts were voiced by Bruce Willis. She also appeared in the 1990 sequel Look Who’s Talking Too.

John Travolta, her co-star in both films, 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 played 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 on Tuesday 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.”

In their statement, Alley’s children remembered her “zest and passion for life, her children, grandchildren and her many animals, not to mention her eternal joy of creating, were unparalleled and leave us inspired to live life to the fullest just as she did”.

They also thanked her fans.

“We thank you for your love and prayers and ask that you respect our privacy at this difficult time,” the statement said.

-with AAP