A California judge on Wednesday scheduled a hearing for porn star Stormy Daniels' lawsuit against Trump and Cohen, in which Daniels seeks to void a nondisclosure pact negotiated by Cohen barring her from discussing an alleged affair with Trump. The hearing is set for Friday morning.
On Monday, Cohen for the first time attended court proceedings regarding an ongoing investigation into potential financial crimes and acts of concealment. A week earlier, Cohen's properties were raided by FBI agents based on a referral from special counsel Robert Mueller, who is investigating purported Kremlin links to Trump's presidential campaign. The seized materials include documents related to Daniels and communication between Trump and Cohen.
In a statement, Cohen's attorney David Schwartz said, "the decision to voluntarily discontinue these cases was a difficult one."
"We believe the defendants defamed my client, and vindicating Mr. Cohen's rights was — and still remains — important. But given the events that have unfolded, and the time, attention, and resources needed to prosecute these matters, we have dismissed the matters, despite their merits," Schwartz said.
Cohen is referenced heavily in the 35-page dossier, and is accused of attending a "secret liaison with the Kremlin" in Prague, among other allegations.
The dossier had reportedly been circulating for some time among news outlets before the 2016 election. But its salacious and unverified claims — including that Russian spies held evidence that Trump paid prostitutes to urinate on a mattress in a Moscow hotel room — were not made public until January, when BuzzFeed published a story about the document.
The White House did not immediately respond to CNBC's request for comment on Cohen's withdrawal from the suit.
Cohen denied the dossier's claims about him, famously allowing news outlets to view his passport as evidence that he had "never been to Prague" in his life.
A report from McClatchy in April, citing two sources familiar with the special counsel's probe of possible Russian links to Trump's campaign, said that Mueller has evidence that Cohen made a trip to Prague in 2016. Cohen again denied the trip.
Disclosure: CNBC parent NBCUniversal is a minority investor in BuzzFeed.