Didier Gailhaguet, the long-serving head of France's skating federation, has resigned after a wave of condemnation following allegations of sexual abuse in figure skating.

Announcing his resignation on Saturday, Gailhaguet denied covering up for a coach accused of rape and sexual abuse by former figure skaters and said no one at the federation was aware of the alleged wrongdoing.

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Speaking after a special meeting of the federation in Paris, Gailhaguet said, "Out of the need for appeasement, I have taken ... the wise decision to resign from my position as president of the federation."

Paris prosecutors opened a criminal investigation this week into accusations from 10-time French champion Sarah Abitbol that she was raped by skating coach Gilles Beyer from 1990-1992, when she was a teen.

Abitbol accused Beyer in a book published last week and has also spoken about her personal experience on television.

Sports newspaper L'Equipe also published accounts of sexual abuse by three other former French figure skaters, and accused the federation of "inaction".

The accusations led to calls for Gailhaguet to resign, notably by France's current Sport Minister Roxana Maracineanu, because Beyer was allowed to continue having roles at the French skating federation until 2018 despite having been let go by the French sport ministry in 2001 following a report highlighting repeated "serious acts" committed against young skaters.

Gailhaguet served a first term as president from 1998 to 2004 and started his second stint in 2007. Four members of the federation's executive office, including a treasurer, resigned on Tuesday night.

Maracineanu had met with Gailhaguet on Monday and asked him to resign, saying he "cannot absolve himself of his moral and personal responsibility".

He defiantly said he would not, and then hit back at Maracineanu in virulent terms when holding a news conference on Wednesday, during which he again said he would not immediately resign.

After finally stepping aside on Saturday, he took another swipe at Maracineanu, maintaining his view that she was making him "a sacrificial victim" for the wrongdoing of others.

Gailhaguet blamed former Sport Minister Marie-George Buffet, who held the position in 2001, saying she allowed Beyer to continue working despite evidence against him.

Gailhaguet controlled of the skating federation when Beyer was named France's team leader during the 2011 Junior World Championships held in Gangneung, South Korea. Gailhaguet said it was "probably through naivety or trust" that he allowed Beyer to be given that role, given serious allegations against him previously.