Disability charity Scope said Borthwick should reflect on what he said and educate himself.
“We hope he takes the opportunity to get to know the reality of disabled people’s lives,” said the organisation’s media manager Warren Kirwan.
In his statement to the Sun on Sunday, Borthwick said: “I want to apologise sincerely and wholeheartedly for the words I used in the video showing my reaction to making it through Blackpool week on Strictly.”
He added: “It is no excuse, but I did not fully understand the derogatory term I used and its meaning.
“That is on me completely.
“Now I am aware, I am deeply embarrassed to have used the term and directed it in the way I did.”
Borthwick rose to fame for his portrayal of Jay Brown (previously Mitchell) in BBC soap EastEnders.
He has starred in it since 2006, making him one of the longest-serving actors on the show.
He has won a British Soap Award for best dramatic performance from a young actor, and an Inside Soap Award for best actor.
The 30-year-old took part in the latest series of Strictly, where he was paired with professional dancer Michelle Tsiakkas.
It marked a return to the ballroom for him, after he won the 2023 Christmas special.