Sylvester Stallone says his late son was the "centre of his universe".
Sage Stallone, 36, was found dead in his Los Angeles home on Friday, and his father has released a black-and-white photograph of him with his late son, taken in 1991.
He has also given a statement about his loss to TMZ.
"When a parent loses a child there is no greater pain. Therefore I am imploring people to respect my talented son's memory and feel compassion for his loving mother Sasha (Czack)," he told the website.
"This agonising loss will be felt for the rest of our lives. Sage was our first child and the centre of our universe and I am humbly begging for all to have my son's memory in full left in peace."
Stallone was referring to the speculation which has been rife about how Sage died.
Prescription medication was discovered near his body, leading to reports he may have overdosed.
No suicide note was found in Sage's home and it has been suggested his death was accidental. A friend of the star's has now claimed he had seemed out of sorts for a while.
"Something just has not been right with Sage for the past months," the insider told Chicago Sun-Times.
"I don't think he would do anything to take his own life, and there's absolutely no evidence he did.
"But I wonder if his overall distraction could have led him to make a mistake. It's mistakes that so often lead people taking prescription drugs to make a fatal mistake."
Over the weekend, there were reports Sage's body lay undiscovered for several days. These claims have been denied by his lawyer and friend George Braunstein.
Much was also made of the actor-director spending increased amounts of time alone at his Hollywood Hills home.
David Finster, who knew the late star, insists there was nothing strange about Sage's living arrangements.
"You can't make much of something like that. Creative people - and Sage was one of the most originally creative people I've ever met - often work best when totally alone, so they can completely concentrate," he said.
An autopsy on Sage's body was conducted on Sunday, with toxicology tests expected back within two weeks.
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