The 56-year-old was found dead at his home in Barnes, southwest London, on Monday.
"We now know that our darling Rik suffered an 'acute cardiac event' at our home around midday on June 9," Barbara Mayall said in a statement.
"He had just returned from his usual run and many people had seen him that morning."
The comedian, who had three children, survived a near-fatal quad bike accident in 1998 but is thought to have suffered afterwards with epilepsy.
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And he took a pop at former Conservative prime minister Margaret Thatcher's government in the role of conniving politician Alan B'Stard in satirical TV series "The New Statesman".
Mayall's daughter Bonnie paid tribute earlier this week to "the man, the myth, the legend -- my wonderful, generous, foul mouthed and hysterical father. My idol now and forever."
"We always knew that Rik was well-loved but we are all overwhelmed by so many joining us in our grief," she said.
Friends also paid their respects by installing an irreverent blue plaque -- a mock-up of those erected on buildings in Britain to remember famous people -- on a bench in London.
"Rik Mayall 1958-2014 Punched his friend in the balls on a bench near this spot," the plaque said.