"I made a mistake which I'm ver sorry for - I'm very sorry for the hurt that I've caused".
Another added: "So, they finally addressed the elephant in the room - and it was the single most cringe-inducing thing I've had the displeasure to watch".
Walsh was in a long-term relationship with actress Humphries, while Jones is married to fellow Strictly star Neil Jones.
Seann and Katya are set to remain on Strictly Come Dancing despite a lot of public pressure calling for the pair to be removed from the competition. "I don't think it's a curse it just happens".
After the pictures were published she said they were in a "very happy" relationship and that the incident was not a reflection on their relationship.
Their apologies come after fans were bewildered as Katya's husband, Neil, ignored the photos and videos of the pair kissing and instead cheered on the dance partners for their performance over the weekend.
She concluded: "But - this whole business has served to remind me that I am a strong, capable person who is now free; and no victim".
It Takes Two airs weeknights at 6:30pm on BBC2.
Michael gaining strength, churning toward Florida
The north Florida city of Tallahassee on Sunday opened two locations where residents could get sandbags in case of flooding. Maximum sustained winds have increased to near 75 miles per hour with higher gusts, the National Hurricane Center said .
Walsh's ex, Rebecca Humphries, has yet to officially react to the broadcast but if her likes on Twitter are anything to go by, it still seems like she's waiting for him to actually say sorry.
Seann has apologised for hurting Rebecca, but he has also defended his own reputation, insisting he's been portrayed unfairly over recent days. "We were getting on well, we were having fun", he said. You never think about the extent of the damage that you're going to do. "Our relationship wasn't ideal, that doesn't mean I wanted it to end the way it finally did".
"This is no excuse but it was a one-off drunken mistake which I am truly sorry for".
"I'm not ideal, far from it, our relationship wasn't flawless".
Appearing to dispute some of the claims his ex Rebecca made in her statement about Seann's previous behaviour during the couple's relationship, Seann explained, "I feel it's also important for me to say that the people that know me the most, that love me, they know that I am not the person I'm being portrayed as".
Will you be watching Strictly on Saturday night? "Despite everything, I hope he gets everything he wants from this".
However, the BBC has stated the dance couple will perform on the show on Saturday.
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