The lawsuit was originally filed in October, and was refiled on Sunday to list Mr Carter as a defendant.
The BBC has contacted Mr Carter’s lawyer, Alex Spiro, and his publicist for comment.
The legal action was filed under New York’s Victims of Gender-Motivated Violence Protection Act, by a Texas-based lawyer, Tony Buzbee.
Mr Buzbee has filed several lawsuits in recent months accusing Mr Combs of assault and rape. The hip-hop artist is due to face a criminal trial on 5 May.
Mr Carter said in a statement posted to social media: “My lawyer received a blackmail attempt, called a demand letter, from a ‘lawyer’ named Tony Buzbee.
“What he had calculated was the nature of these allegations and the public scrutiny would make me want to settle.
“No sir, it had the opposite effect! It made me want to expose you for the fraud you are in a VERY public fashion. So no, I will not give you ONE RED PENNY!!”
A statement from Mr Combs’s legal team said this amended lawsuit was the latest in a series of “shameless publicity stunts, designed to extract payments from celebrities who fear having lies spread about them, just as lies have been spread about Mr Combs”.
The statement said that the judicial process would show Mr Combs to be innocent of all the allegations against him. He faces 30 other lawsuits.
Responding to the criticism, Mr Buzbee posted a picture of himself to his Instagram as a younger man in military uniform, with a caption saying he had faced “a coordinated and aggressive effort” to stop him from bringing the case forward.
“I also won’t allow anyone to scare my clients into silence,” he wrote. “Sunlight is the best disinfectant and I am quite certain the sun is coming.”
- The charges against Sean ‘Diddy’ Combs explained
The accuser in Sunday’s legal filing, who is identified only as “Jane Doe”, said that in 2000, when she was 13, a friend dropped her off at the VMAs at Radio City Music Hall in Manhattan.
She approached limousine drivers outside the venue to try to gain access to the show, according to the legal action.
One driver told her that he was employed by Mr Combs and that she “fit what Diddy was looking for”, says the lawsuit.
Later that evening the chauffeur drove her to a party at a white house, according to the legal action.
