Cohen, in the same email obtained by ABC News, also called out the Trump administration for instituting a policy of separating children from parents who cross the U.S.-Mexico border illegally.
"As the son of a Polish holocaust survivor, the images and sounds of this family separation policy is heart-wrenching," Cohen wrote.
"While I strongly support measures that will secure our porous borders, children should never be used as bargaining chips."
Trump on Wednesday signed an executive order that he says would keep immigrant families together if they are detained after crossing the Mexico border.
Cohen's criticism of the president's policy is striking. He has been known as a hardcore Trump loyalist.
But in recent weeks, speculation has grown that Cohen will agree to cooperate with federal investigators and possibly give them information about Trump in a bid to limit his legal exposure.
CNN reported Wednesday that Cohen has let friends know he is prepared to turn over information about Trump to prosecutors.
"He knows a lot of things about the President and he's not averse to talking in the right situation," a Cohen friend told CNN. "If they want information on Trump, he's willing to give it."
Another friend quoted by the news site said, Cohen "feels let down by [Trump] and isolated by him."
Cohen did not return a request for comment from CNBC.
Venture capitalist Elliott Broidy resigned as deputy finance chairman of the RNC in April. His departure came shortly after The Wall Street Journal revealed that Broidy, who is married, had agreed to pay a Playboy Playmate $1.6 million after she claimed to have been impregnated by him. Sources have told CNBC that Cohen was paid $250,000 for negotiating and handling that deal for Broidy.
In February, the RNC's then-national finance chairman, casino mogul Steve Wynn, resigned after a Journal report revealed that he had been accused of sexual misconduct.
Cohen, 51, is being investigated by prosecutors in New York for a variety of business-related dealings, as well as a $130,000 hush money payment he made to porn star Stormy Daniels shortly before Election Day 2016. Daniels says the payment was made to keep her quiet about an affair she had with Trump a decade before.
Files related to Daniels were among the documents seized April 9 by FBI agents during a raid on Cohen's apartment and office, as a well as on a hotel room where he and his family were staying during renovations of their residence.
The White House has denied the president had sex with the actress.
Cohen, who has not been charged, reportedly has hired a new criminal defense lawyer, Guy Petrillo, to represent him as prosecutors continue their probe. Petrillo previously served as chief of the criminal division of the U.S. Attorney's Office for the Southern District of New York, the same division now investigating Cohen.