LOS ANGELES — Donald J. Trump never signed the nondisclosure agreement lawyers had presented in 2016 to a pornographic-film actress, rendering it null and void, according to a lawsuit filed on Tuesday by a lawyer for the actress.

The filing, in Los Angeles Superior Court, represents the latest development in a legal battle involving Mr. Trump, his longtime personal lawyer and the actress, Stephanie Clifford, whose stage name is Stormy Daniels.

The lawsuit came days after Michael D. Cohen, Mr. Trump’s personal lawyer, had legally pressured Ms. Clifford, initiating arbitration proceedings against her in Los Angeles in efforts to prevent her from speaking out about an affair she said she had with Mr. Trump, according to the complaint.

The suit, a copy of which was obtained by The New York Times, alleges that Mr. Trump “purposely did not sign the agreement so he could later, if need be, publicly disavow any knowledge of the Hush Agreement and Ms. Clifford.”