Sheen told David Letterman on CBS' "The Late Show" on Thursday that their relationship has since rebounded.
"We're working toward getting back together and fixing things," the 40-year-old actor said.
It would be a dramatic U-turn for a relationship that publicly disintegrated just months before Richards, 34, gave birth to the couple's second child.
"It's the first time I got dumped in my life," Sheen said. "I think the one thing I would point to as a primary reason, basically, is that I was a gigantic ass."
The couple were married in June 2002. They met while shooting the independent film "Good Advice" in 2000 and appeared in 2003's "Scary Movie 3."
"I had to take a step back and really take a look at myself and the situation," Sheen said. "I made a commitment to this woman that I love, this family that I love and I realized this can be fixed."
"Things are really good," he said. "Today we have hope, we have a shot."