The deal involving Mr. Broidy was not known to be a subject of the federal investigation. It is unclear whether the F.B.I. has scrutinized Mr. Davidson, who is no longer representing the former Playboy model. Her new lawyer is Peter K. Stris, who also now represents Ms. McDougal.
In his statement, Mr. Broidy apologized to his wife and family while acknowledging that he had had an affair with the woman, who has not been identified. He said that “she alone decided that she did not want to continue with the pregnancy, and I offered to help her financially during this difficult period.”
He lamented that the issue had become a national news story, which he attributed to the publicity surrounding the federal investigation of Mr. Cohen. He said that the lawyer “reached out to me after being contacted by this woman’s attorney, Keith Davidson,” and that he hired Mr. Cohen after Mr. Cohen “informed me about his prior relationship with Mr. Davidson.”
In fact, the contract in Mr. Broidy’s case included the same aliases that were used in the 2016 contract with Ms. Clifford — “David Dennison” and “Peggy Peterson” — according to a person familiar with it.
A spokesman for Mr. Davidson said he could not confirm or deny the details of the agreement. In a statement, Mr. Davidson said, “I’ve always acted in my client’s best interest, and appropriately in all matters.”
Mr. Cohen declined to comment.
Mr. Davidson’s relationship with Mr. Cohen forms part of the basis for a lawsuit Ms. McDougal has filed seeking to get out of her contract with A.M.I.; The Enquirer never ran her story after buying it in August 2016.
In the lawsuit, she contends that Mr. Cohen played a secret role in the negotiations for that deal, though he had no formal reason to be involved, given that the talks were between Ms. McDougal and the tabloid media company. The Times reported earlier this year that Mr. Cohen and Mr. Davidson discussed the deal the day before Ms. McDougal signed the contract.
Mr. Broidy was a national deputy chairman of the R.N.C.’s finance committee, a title he shared with Mr. Cohen, who remains in that role. Mr. Broidy is the second member of that committee to resign this year amid questions involving their behavior with women and deals to silence them. In January, the casino magnate Stephen Wynn stepped down from the committee’s chairmanship after allegations of sexual misconduct surfaced against him, one resulting in a settlement of $7.5 million.
Mr. Broidy was a major fund-raiser for former President George W. Bush, but he is particularly connected in Mr. Trump’s orbit.
He got his start in business as an accountant and then as an investment manager for Glen Bell, the founder of Taco Bell. He was a vice chairman of Mr. Trump’s inaugural committee, has met frequently with top White House officials and had an Oval Office meeting with the president in October, according to documents obtained by The Times.
During the wide-ranging October meeting, Mr. Broidy raised numerous topics high on the agenda of the United Arab Emirates, a country that has given his security company a contract worth hundreds of millions of dollars. He pitched the president on a paramilitary force his company was developing for the U.A.E. and urged Mr. Trump to fire Rex W. Tillerson, then the secretary of state, who the U.A.E. believed was insufficiently tough on its rival Qatar.
The documents show that Mr. Broidy has worked closely with George Nader, an adviser to the U.A.E. and a witness in the special counsel’s investigation, to help steer Trump administration policy on numerous issues in the Middle East. Robert S. Mueller III, the special counsel, is examining Mr. Nader’s possible role in funneling Emirati money to finance Mr. Trump’s political efforts. There is no indication that Mr. Mueller’s team is looking into Mr. Broidy.
In 2009, Mr. Broidy pleaded guilty to charges that he made nearly $1 million worth of illegal gifts to New York State officials in order to win an investment of $250 million from the state’s public pension fund. Among the gifts were trips to Israel and Italy, payouts to officials’ relatives and girlfriends and an investment in one relative’s production of a low-budget movie called “Chooch.”