Arkin was named best supporting actor for his role in Little Miss Sunshine at the Academy Awards in 2007.

He died on Friday at his home in Carlsbad, California.

Douglas, who appeared alongside Arkin in the Emmy-nominated Netflix comedy series The Kominsky Method, wrote on Instagram: "Today we lost a wonderful actor whose intelligence, sense of comedy and consummate professionalism over the past 70 years has left an indelible mark on our industry.

"My experience of working with Alan were some of my most memorable. He will be deeply missed."

John Cusack, who starred with Arkin in Grosse Pointe Blank in 1997 and America's Sweethearts in 2001, said he was "so sad".

He added on Twitter: "My thoughts are with his son Adam and all his loved ones - your father spread light everywhere he went - every experience I had with him.

"I feel like he challenged me to be a better person just by sharing his insights into humans... his wicked sense of humor, his intelligence and by his presence alone - what a guy."

Billy Crystal also described Arkin as "one of our greatest actors".

The When Harry Met Sally star added: "Hilarious, heartbreaking, and the ability to be terrifying, his range was amazing. I cherish the chance I had to act with him in America's Sweethearts."

'He was adored'

Arkin's sons Adam, Matthew and Anthony said in a joint statement: "Our father was a uniquely talented force of nature, both as an artist and a man.

"A loving husband, father, grand and great grandfather, he was adored and will be deeply missed."

Arkin appeared in more than 100 films and TV shows.

He was nominated for an Academy Award four times, including in the best supporting actor category for Argo.

Other Hollywood names paying tribute included Rosemary's Baby actress Mia Farrow, who said she was "very sad".

She added: "Such a lovely person - of course, a great actor. It was a privilege to work with him in The Last Unicorn. For me he will always be 'Schmendrick' my invaluable magician companion on our search for other unicorns."

Michael McKean, who starred in This Is Spinal Tap and Better Call Saul, also recalled his time working with Arkin.

He wrote on Twitter: "When I was a young actor people wanted to know if I wanted to be a serious actor or a funny one. I'd answer 'Which kind is Alan Arkin?' and that shut them up."

McKean added: "Charming, hilarious, and armed with a flawless b******* detector, he was pure pleasure to be with."

Aliens and Beverly Hills Cop actor Paul Reiser also wrote: "A world without Alan Arkin is... not so great... Getting to know him - and getting a laugh out of him - is a highlight of my life. RIP dear friend."

While Seinfeld actor Jason Alexander described him as "a wonderful, original voice for comedy" and "a kind and generous soul".

'The best rejection I ever got'

Arkin was initially turned down for his award-winning role in Little Miss Sunshine because the directors thought he looked too fit and healthy.

In the film, he played a foul-mouthed 80-year-old grandfather who was frail and shaky from years of drug abuse.

"It's the best rejection I ever got in my life - they thought I was too virile," Arkin told The New York Times in a 2007 interview - during which he jokingly flexed his biceps and struck a bodybuilder pose.

He landed his first Oscar nomination - for best actor - in his debut major film role in 1966, when he played a Soviet sailor in Cold War comedy The Russians Are Coming! The Russians Are Coming!

Arkin also received praise for his performance as a psychopathic killer in the 1967 film Wait Until Dark opposite Audrey Hepburn.

He later said the experience made him feel uncomfortable because he "didn't like being cruel to her".

Arkin's big screen appearances also included the 1970 film version of Catch-22 and Edward Scissorhands in 1990.

Most recently, he voiced the character of villain Wild Knuckles in last year's animated hit Minions: The Rise of Gru.

Arkin was also a director, musician, author and stage performer, winning a Tony Award in 1963 for his major role in Carl Reiner's Enter Laughing.