The pair played mother and daughter in Absolutely Fabulous for five series of the hit sitcom, as well as in the 2016 film.
Saunders penned the series, based on a sketch she created with Dawn French, and asked Dame June to play Edina Monsoon's mother.
In a statement to the Press Association, Saunders said: "It's so tremendously sad to lose June. I will always be grateful that she agreed to be in Ab Fab and even more grateful that she became a dear friend.
"She lived and worked with an extraordinary grace. Everything June did was perfectly measured. She was so loved and I will miss her hugely."
Dame June "passed away peacefully" on Friday, according to her agent.
Heartfelt tributes have been paid to the talent and warmth of the star, whose career in acting spanned eight decades.
During her life in showbusiness, she tackled bawdy comedy in the Carry On films, and starred in the long-running sitcom Terry And June, as well as Absolutely Fabulous.
Julia Sawalha, who played her on-screen granddaughter Saffy, paid tribute to her friend and teacher in an online post, calling her "Gran".
She said: "Thank you #damejunewhitfield, for teaching me my craft with such grace and dignity.
"I always wanted you to know how in awe of you I was, however, you were always far too humble to accept my adoration.
"You were a great source of inspiration to me. Bye-bye Gran."
Joanna Lumley, who played Edina's hard-drinking and promiscuous friend Patsy Stone, said she was "heartbroken" by her death.
Lumley told ITV News: "I am heartbroken to lose such a darling friend and shall never forget her sensational talent, humour and her generosity to us all who had the joy of working with her on Ab Fab.
"She will always have a most special place in my heart."
Fellow TV comic actor David Walliams also offered his appreciation for the talents of Dame June, calling her achievements in entertainment "brilliant".
He wrote: "June Whitfield's incredible career in British comedy stretched all the way from 'Hancock's Half Hour' to 'Absolutely Fabulous'. She was always there, always being brilliant."
And Spice Girls singer Emma Bunton paid her own tribute to Dame June, who made her feel comfortable on set when she appeared in Ab Fab
She wrote on Twitter: "So sad this evening. Such an incredible lady with the warmest heart. I was so nervous working with her but she had a way of making you feel comfortable and special Thank you Dame June Whitfield."