Alley debuted on the NBC sitcom in 1987 as Rebecca Howe, quickly becoming a fan favourite for her role opposite Ted Danson's womanising bar owner Sam Malone.

Grammer, who played the psychiatrist Frasier Crane alongside Alley in Cheers, admitted he had loved the actress.

"I always believed grief for a public figure is a private matter but I will say I loved her," the 67-year-old said in a statement provided to the PA news agency.

In a separate statement provided to PA, Perlman said she had "never met anyone remotely like" Alley, adding that she would miss her "very, very much".

"Kirstie was a unique and wonderful person and friend. Her joy of being was boundless," Perlman, who played head waitress Carla Tortelli on the show, said.

"We became friends almost instantly when she joined the cast of Cheers. She loved kids and my kids loved her too.

"We had sleepovers at her house, with treasure hunts that she created. She had massive Halloween and Easter parties and invited the entire crew of the show and their families.

"She wanted everyone to feel included. She loved her children deeply.

"I've never met anyone remotely like her. I feel so thankful to have known her. I'm going to miss her very, very much."

Alley's death was announced by her family, who described her as an "amazing mother and grandmother".

John Travolta, who starred with Alley in the trilogy of Look Who's Talking films, said his time with the actress represented "one of the most special relationships I've ever had".

Sharing a picture of the pair together on Instagram, Travolta wrote: "Kirstie was one of the most special relationships I've ever had. I love you Kirstie. I know we will see each other again."

Jamie Lee Curtis said the pair had a "mutual respect and connection" when they worked together in more recent years on the comedy horror series Scream Queens.

"I've just heard the sad news that Kirstie Alley has died," the actress wrote, sharing a picture of them together.

"She was a great comic foil in Scream Queens and a beautiful mama bear in her very real life. She helped me buy onesies for my family that year for Christmas.

"We agreed to disagree about some things but had a mutual respect and connection. Sad news."

Horror director John Carpenter described Alley as a "delightful actress".

"Kirstie Alley was a delightful actress I had the pleasure to work with on VILLAGE OF THE DAMNED. She will be missed," he wrote.

Alley starred in the 1995 US science fiction-horror film alongside Christopher Reeve, Linda Kozlowski, Michael Pare and Mark Hamill.

Living Colour founder and guitarist Vernon Reid said Alley had "defined relatable" with her on-screen performances.

The English-American musician tweeted: "A lot of us are bummed right now. I can feel it. Kirstie Alley defined 'relatable'.

"Beautiful and funny is not easy to pull off. Kirstie Alley was part of a small pantheon of the fearless and shameless.

"She always told her truth on screen. In our TV rooms. She is missed. Realtime."

Australian Associated Press