Rik Mayall's wife says the comedian "suffered an acute cardiac event" before his death at their home on Monday.
Barbara Robbins said it happened after the comic returned from a morning run.
Her comments follow the West London Coroner's Office saying the post-mortem examination had proved inconclusive and further tests were required.
A pioneer of the 1980s alternative comedy scene, Mayall starred in shows including The Young Ones and Bottom.
In a statement, Ms Robbins said: "We now know that our darling Rik suffered an 'acute cardiac event' at our home around midday on June 9th.
"He had just returned from his usual run and many people had seen him that morning."
She also thanked the public for their messages of support and the press "for their discretion at this time and for all the wonderful coverage that you have given Rik - it would have made him very happy".
"We always knew that Rik was well loved but we are all overwhelmed by so many joining us in our grief," she added.
Mayall's daughter Bonnie paid tribute to her "generous, foul-mouthed and hysterical father" in a Facebook post.
"My dad was loved not only by my family, but by many many others. We will never forget him and neither will the world.
"RIP to the man, the myth, the legend. My idol now and forever. We love you daddy."
Police were called to Mayall's house in Barnes, south west London, shortly after lunch on Monday 9 June. "A man, aged in his 50s, was pronounced dead at the scene," a spokesman for Scotland Yard said.
He added the death was not believed to be suspicious.
Mayall began his career on stage with Adrian Edmondson, and went on to create and co-write anarchic sitcom The Young Ones.
His later roles included Lord Flashheart in Blackadder and sneering politician Alan B'stard in The New Statesman.
Tributes flooded in after his death, with Ben Elton saying he "changed my life utterly when he asked me to co-write The Young Ones with him".
"He always made me cry with laughter, now he's just made me cry."
Edmondson, who also appeared with Mayall in Bottom and a stage production of Waiting For Godot, recalled their "carefree, stupid" partnership.
"There were times when Rik and I were writing together when we almost died laughing," he said.
"And now he's died for real. Without me. Selfish bastard."
Nigel Planer, who played Neil in The Young Ones, said he was "very, very sad and upset that we've lost Rik, who was inspirational, bonkers, and a great life force".
Stephen Fry said he was "distraught" upon hearing of Mayall's death, calling him "an authentic comedy genius and a prince among men".
Mayall is set to appear in this weekend's Official Chart countdown, after a social media campaign encouraging fans to honour his memory by downloading a track he recorded for the 2010 World Cup.
The song, Noble England, failed to chart at the time of release but reached 38 in the midweek sales chart.
By Thursday morning, it was sitting just outside the top 10, the Official Charts Company reported.
"Rik Mayall's death this week was a shock to a whole generation of comedy fans - and their reaction in pushing his 2010 single is a reflection of how much he was loved," commented Official Charts Company chief executive, Martin Talbot.
The singer previously scored a UK number one in 1986, appearing with Cliff Richard and the cast of The Young Ones on a cover of Living Doll.
His spoof hair metal band, Bad News, which also featured Planer and Edmondson, also scored low-ranking chart hits in the 1980s.
Their eponymous debut album reached number 69, while a shambolic, off-key rendition of Bohemian Rhapsody charted at 44.