Actor Isaiah Washington has issued an apology in a statement to People for his behavior during the now-infamous on-set argument with a Grey's Anatomy co-star.

"I sincerely regret my actions and the unfortunate use of words during the recent incident on-set," he said. "Both are beneath my own personal standards. I have nothing but respect for my co-workers, and have apologized personally to everyone involved."

After Washington, 43, and Patrick Dempsey, 40, clashed on October 9, reports began surfacing that Washington had used a homophobic slur during the fracas.

Then on October 19, their co-star, T.R. Knight, disclosed that he is gay.

"I'd like to quiet any unnecessary rumors that may be out there," he said. "I hope the fact that I'm gay isn't the most interesting part of me."

Fallout from the turmoil has sparked talk of everything from hasty script rewrites of an impending onscreen fight scene (not true, says show creator Shonda Rhimes) to rumors that Washington would be fired and replaced by former ER star Eriq La Salle.

"I found (those rumors) not only ridiculous but offensive that we would consider replacing a member of our family. Also, the (idea) that one black man was interchangeable with another is disturbing to me," Rhimes said.

Rhimes also dismissed speculation that the mood on the set has been tense since the argument.

"The mood's what the mood's always been," she said. "We have a group of people who are more of a family than anything else. We have our fun days, and we have our days when people are tired and the work is hard."

On Tuesday's episode of The Ellen DeGeneres Show, Grey's costar Katherine Heigl played down the incident, calling it a "scuffle" that blew over in a matter of a few minutes.

Washington was scheduled to tape an interview with DeGeneres on Tuesday to air Wednesday, but canceled -- citing a scheduling conflict -- after Heigl jokingly warned DeGeneres to "step back" during Washington's appearance.

So what actually happened between Washington and Dempsey? A set source says that when Knight, 33, was late to film a scene, a debate ensued between Dempsey and Washington, with Dempsey insisting on waiting for Knight before starting the scene. The argument intensified, and the source says that the alleged slur was used -- but Knight was not present.

"Isaiah was running his mouth off," the source told People. "Isaiah verbally attacked Patrick. He tore into him. Patrick's voice escalated and he told Isaiah to f*%k off, (but) that was as heated as Patrick got."

As of today, Rhimes tells the magazine, Dempsey and Washington "are fine" -- as are Washington and Knight.

"They've had conversations," says Rhimes. "They did a really great scene together the other day." The whole affair, she says, "was four and a half seconds of one day in three years. I feel like we've already moved on."

We're glad that Washington and Rhimes have come forward to address the issue and assure us that everything has been resolved. Hopefully, the matter can now be put to bed and we can focus on the show!

Steve Marsi is the Managing Editor of TV Fanatic. Follow him on Google+ or email him here.