Clifford has claimed she had sex with Trump once and then carried on a subsequent yearslong platonic relationship. She has also, through a lawyer, denied the two had an affair. Cohen has denied there was ever an affair.
Cohen has said he paid the porn actress $130,000 out of his own pocket as part of the agreement. He has also said that "neither the Trump Organization nor the Trump campaign was a party to the transaction with Ms. Clifford, and neither reimbursed me for the payment, either directly or indirectly."
The lawsuit charges that the "hush agreement" is legally invalid because it was only signed by Clifford and Cohen. The agreement refers to Trump as David Dennison and Clifford as Peggy Peterson, but an attached exhibit details their true identities.
Clifford's lawsuit also alleges that Trump and Cohen "aggressively sought to silence Ms. Clifford as part of an effort to avoid her telling the truth, thus helping to ensure he won the Presidential Election."
"To be clear, the attempts to intimidate Ms. Clifford into silence and 'shut her up' in order to 'protect Mr. Trump' continue unabated," the lawsuit said. Clifford alleges that as recently as last week, Trump's attorney tried to initiate an arbitration proceeding against her.
Neither Cohen nor the White House immediately responded to requests for comment Tuesday evening.
NBC News first reported the existence of the lawsuit.
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Associated Press writer Jill Colvin in Washington contributed to this report.