Federal prosecutors have given immunity to the company that publishes The National Enquirer in connection with the $150,000 hush-money payment the supermarket tabloid gave Karen McDougal, the Playboy model who claims she had an affair with President Donald Trump. That payment to McDougal was made shortly before the 2016 presidential election and was done "to influence" that election, which sent Trump to the White House, according to the United States Attorney's Office for the Southern District of New York. The SDNY revealed its "non-prosecution agreement" with Enquirer publisher American Media Inc. on Wednesday, shortly after Trump's former lawyer Michael Cohen was sentenced to three years in prison in U.S. District Court in Manhattan. The agreement, which was signed on Sept. 21, requires AMI to cooperate fully with the SDNY's investigations. Read the non-prosecution agreement with the publisher of The National Enquirer Cohen's crimes included his playing a key role in getting AMI to pay off McDougal and his personally paying another purported paramour of Trump's, porn star Stormy Daniels, right before the election to keep quiet about their alleged past trysts with Trump.

Karen McDougal, Playboy Playmate of the Year 1998. Getty Images

One of the counts against Cohen was "causing an unlawful campaign contribution" to be made; that count relates to AMI's payment to McDougal. Another count related the payment to Daniels. The White House has denied Trump had sex with either woman. AMI admitted it paid off McDougal to keep her from publicizing her "damaging allegations" of having had a lengthy affair with Trump a decade before the 2016 election, the prosecutors' office said. The company also admitted "it made the $150,000 payment in concert with" Trump's campaign, according to the SDNY. "AMI further admitted that its principal purpose in making the payment was to suppress the woman's story so as to prevent it from influencing the election," prosecutors said. AMI did not immediately respond to a request for comment from CNBC. Former federal prosecutor Mimi Rocah told MSNBC that AMI's admission cripples Trump's ability to claim that the payment to McDougal was not about the election, and thus not subject to federal campaign finance law rules.

David Pecker, Chairman and CEO of American Media Marion Curtis | AP