He explained: “There are still questions that remain unanswered regarding the circumstances of his death.”
“Our understanding at this stage is that Owain passed suddenly, naturally and peacefully.”
The late actor’s family has been “deeply” moved by the messages of support since his death, while they also hailed him “a brother to so many others”.
He continued: “The outpouring of messages we have received over the past few days has been deeply moving and a testament to the impact he had on so many lives.
“Owain was fortunate enough to have more than one family.
“Alongside his biological one, he built extraordinary, family-like bonds with many of his closest friends, colleagues and loved ones.
“I am incredibly proud that, while he was my brother, he was also a brother to so many others.
“We know that this loss will be felt by a great many people, and we take comfort in knowing how loved he was.”
Owain’s most recent film was indie project La Fantasia.
As well as his big screen roles, he also appeared in West End shows like Mamma Mia! and The Wizard of Oz.
Owain’s fellow stars have paid tribute to him after the news of his death.
Downton Abbey’s Joanne Froggatt wrote: “No words seem to convey my emotions. I am so sorry for your loss and the grief you must be feeling.
“I am devastated to lose our beautiful friend, he was more than a friend, he was joy and life and talent and kindness and fun and intelligence.
“He was everything and my brain can’t compute that we don’t get to hug him again. What I would give for one more hug. You’re forever in our hearts cariad.”
Hayley Tamaddon, who is known for British soap Coronation Street, added that it was “heartbreaking to hear that my beautiful friend has passed away”.
She said: “Owain was loved by so many. He lit up every room he went into.
“I have some wonderful memories of us together, we go back so many years. but our time together in LA will always make me smile.
“Sleep well my love. My heart goes out to his friends, and family Rhodri and Conway.”
Saturday Night Live writer Humphrey Ker, who has appeared on Welcome to Wrexham, wrote: “My friend Owain has died. Unexpectedly and most unwelcomely.
“He was a gentleman and a wally and a talent and a giver and maker of joy. I shall miss him very much.
“I shall, in the brilliant words of Jack Rooke: ‘Not let the injustice of what could have been override all the joy of what was.’”