"You are loved, you count, you matter," Koenig's mother Judy Koenig said Wednesday, addressing her son from police headquarters in Vancouver, British Columbia, 10 days after he was last seen.
His father, "Star Trek" actor Walter Koenig, added: "I just want to know you're OK. If it means you just want to stay here, that's OK. You don't have to come back. Just let us know that's your intention."
"We think he's probably in a very depressed state," Judy Koenig told reporters.
Walter Koenig told the media his son stopped taking anti-depressants a year ago.
Asked if Koenig might try to hurt himself, Walter Koenig replied, "I think it's almost impossible not to explore that as one of the options."
Then, with tears welling in his eyes, he added, "There are so many people out there who really care about him."
Later, on Wednesday night, Walter and Judy Koenig were scheduled to appear on "Larry King," but, for reasons unknown, left the set just before the interview.
"For some reason unbeknownst to anyone, Walter Koenig, the father of the missing Andrew Koenig, and Judy Levin-Koenig... left the studio in Vancouver," King said during the broadcast.
"We checked them out, they were prepared to go on, I said 'hello,' they said 'hello,'" he continued. "We said we'd be on in two minutes, they said 'fine.' And they got up and left, for reasons unknown."
Koenigs' parents went public with their concern for their son earlier in the week when they appeared on "Good Morning America" and the "Today" show. Koenig's sister Danielle appeared on CBS' "The Early Show" and "Larry King Live."
Vancouver police constable Tim Fanning is hopeful that Koenig will see the outpouring of love and concern from his family and friends and get in touch with them.
"We're hopeful that Andrew is still fine, that we're going to find him safe and sound," Fanning told ABC News. "It's a mystery right now. Here's a guy always in contact with family and friends and all of a sudden he cuts off all that contact. Perhaps he wants to just lay low."
Fanning said police do not suspect foul play.
Koenig, 41, who played Richard "Boner" Stabone on the 1980s sitcom, was reported missing by his parents Feb. 18.
Vancouver police say he was visiting friends in West Vancouver when he disappeared Feb. 14. He did not show up for his return flight to California two days later.
That same day, Feb. 16, Walter Koenig who played Chekov on "Star Trek," received a letter from his son, which concerned him because of its "despondent tone."
"He's been depressed," he told ABC News. "He's trying to get ahead in this business and he's been working at it a long time."
Koenig largely dropped out of the spotlight after playing the role of the goofy sidekick to actor Kirk Cameron's Mike Seaver on "Growing Pains." After several smaller movie and television roles, he found work as a video producer and editor.
Lance Miccio, who has known Koenig for seven years and collaborated with him on multiple projects, said Koenig's depression was "something he dealt with."