Simmons, 67, called into the Today show on Monday to say, "Not to worry, Richard's fine."
"No one is holding me in my house as a hostage," he said, noting that he is in good health. "I do what I want to do as I've always done."
"I've taught, like, thousands and thousands of classes and, you know, right now I just want to sort of just take care of me," he said. "I just really don't want to do anything. I just don't want to be traveling anymore. It certainly has taken its toll on me."
He added: "You haven't seen the last of me. I'll come back and I'll come back strong."
The fitness instructor has retreated from the spotlight in recent years, causing the New York Daily News to investigate claims that Simmons is being held inside his home – purposely kept away from his close friends and family – against his will.
In the article, published on Saturday, several friends reportedly told the Daily News that they hadn't heard from Simmons since 2013 and are "very concerned."
However, the star told Entertainment Tonight Online on Sunday that he is not in any danger, and added that the Daily News's report is "very hurtful"
"I am not kidnapped," Simmons said. "I am just in my house right now."
"No one should be worried about me," Simmons told ET. "The people that surround me are wonderful people who take great care of me."
Simmons said he simply needed some time alone and away from the spotlight.
"For the last 40 years I have been traveling, teaching classes and I had a knee injury, so I had a knee replacement, which was very difficult for me," he told Today. "I have really just been taking it easy, staying at home, working out in my gym and doing the things I haven't done in a very long time."
Just one day before speaking out himself, Simmons' rep, Tom Estey, told PEOPLE that the rumors are "untrue and preposterous."
The rep said Simmons is "taking a break from the public eye" and is working on "several projects" that will be announced soon.