A former Playboy model who claimed she had an affair with Donald J. Trump sued on Tuesday to be released from a 2016 legal agreement restricting her ability to speak, becoming the second woman this month to challenge Trump allies’ efforts during the presidential campaign to bury stories about extramarital relationships.

(Read the complaint.)

The model, Karen McDougal, is suing The National Enquirer’s parent company, which paid her $150,000 and whose chief executive is a friend of President Trump’s. The other woman, the adult entertainment star Stephanie Clifford, better known as Stormy Daniels, was paid $130,000 to stay quiet by the president’s personal lawyer, Michael D. Cohen. She filed a lawsuit earlier this month.

Both women, who argue that their contracts are invalid, are trying to get around clauses requiring them to resolve disputes in secretive arbitration proceedings rather than in open court. Mr. Trump has denied the affairs, which both women have described as consensual.

In other potential legal trouble for the president, a Manhattan judge on Tuesday denied a move by Mr. Trump’s lawyers to block a defamation suit from Summer Zervos, a former “Apprentice” contestant. She accused Mr. Trump of sexually harassing her after she appeared on his reality show. He has called her and over a dozen other women who accused him of harassment “liars.”