The Associated Press reported this week that Veselnitskaya worked more closely with senior Russian government officials than she previously let on, based on scores of emails, transcripts and legal documents that show her to be a well-connected attorney who served as a ghostwriter for top Russian government lawyers and received assistance from senior Interior Ministry personnel in a case involving a key client.
CNN cited anonymous sources saying Cohen was willing to share that information with special counsel Robert Mueller, who is investigating possible collusion between Trump's campaign and Russian Federation. The Trump Org CFO also set up a monthly retainer through the company that was used to reimburse Cohen for the $130,000 hush money payment to Stormy Daniels.
His comments come amid an ongoing political storm in the United States, where reports have emerged claiming that Mr Trump did know in advance about a meeting between his son and Russian agents.
"Usually you don't discuss joint defense agreements, but i think it's obvious there's been so much public discussion that there isn't one right now", Giuliani said.
The Thursday report of Cohen's claims is further proof that Cohen could flip on Trump in the Mueller investigation - which would be a nightmare for Trump's legal team.
Mr Cohen did not immediately return a request for comment on Mr Trump's tweet.
"Did you inform your father about the meeting or the underlying offer prior to the meeting?"
"(Cohen) even retained Bill and Crooked Hillary's (Clinton) lawyer", Trump also wrote, referring to Davis.
Earlier this week, Davis gave CNN a recording of a conversation that was secretly taped by Cohen shortly before the 2016 presidential election. U.S. intelligence agencies say Russian Federation interfered to support Trump's candidacy.
Cohen says he was one of several people with Trump when Trump Jr. informed him of the offer, and Trump said he should go ahead with the meeting.
Andrew McCarthy, a former assistant US attorney for the Southern District of NY who is now a contributing editor for National Review and a Fox News contributor, told Fox News host Laura Ingraham that "the big problem" Cohen will face concerns his "prior testimony" and "prior interviews", in which he "evidently did not cough this" information up. "I would not accept him in a case as a witness, as a prosecutor", he added later.
However, Rivera added that it is a "shaky proposition" that Trump had knowledge of a Trump Tower meeting between son Donald Jr. and a Russian national, as Cohen has posited.
The president's son testified before Congress that he didn't tell his father, according to a transcript released by the Senate Judiciary Committee. At 4:04 p.m. on that day, phone records show that Agalarov called Trump Jr.; the call lasted up to 2 minutes.
The facts surrounding the Trump Tower meeting have always been a point of interest. "We are very confident of the accuracy and reliability of the information that has been provided by Mr. Trump, Jr., and on his behalf". Trump Jr. says he didn't get any dirt at the meeting - and the promised speech never happened.