By Pamela Brown and Sophie Tatum, CNN

(CNN) -- Rudy Giuliani said Thursday the latest revelations on Michael Cohen misleading Congress about his business dealings with Russia during the 2016 campaign on behalf of the Trump Organization have "no contradiction" to what President Donald Trump has already said to special counsel Robert Mueller's team.

Giuliani, the former New York mayor who currently serves as Trump's lawyer, said Mueller did ask about the proposed Trump Tower Moscow deal, which Cohen had previously said had ended in January 2016 ahead of the Iowa caucuses.

When asked about Trump's knowledge of the business deal at the time, Giuliani said, "As far as he knew, there was a proposal -- he did discuss it with Michael Cohen and signed a non-binding letter of intent and it never went beyond that."

The President's written answers to the Mueller team's questions were broad and not specific to when he was told things about the project, Giuliani said.

Giuliani also told CNN that "neither of the two versions from Michael Cohen creates a problem for what the President testified."

Earlier Thursday, Cohen pleaded guilty to making false statements to Congress about the Russia investigation in a charge brought forward by Mueller. Cohen's guilty plea suggests he has had more involvement with the special counsel than was previously known.

When asked whether he thought the special counsel team -- which he referred to as "out of control prosecutors" -- intentionally waited to get the President's written answers to questions from the Russia probe before charging Cohen, Giuliani said, "It could be."

He added, "Their sneakiness didn't work if that's what they were trying to do."

Trump on Thursday responded to the news that Cohen had pleaded guilty, calling his former attorney "a weak person," before leaving for the G20 Summit in Buenos Aires.

"He was convicted with a fairly long-term sentence with things unrelated to the Trump Organization," Trump said, citing Cohen's legal issues with mortgages and the IRS. In fact, Cohen hasn't been sentenced in either case, and the charges to which he pleaded guilty in August included information about his reimbursement by the Trump Organization for payments he made or helped orchestrate to conceal allegations from two women about sexual encounters with Trump before he ran for office. Trump has denied those claims.

Giuliani said the special counsel's office was not showing any sensitivity to the President's schedule by having Cohen plead just before Trump left for the G20, saying it was "deliberately or negligently" interfering with the President.

Cohen's appearance in court on Thursday came just days after Mueller's team said another former Trump confidant had lied to the special counsel two months after having agreed to cooperate.

On Tuesday, prosecutors said in a filing that former Trump campaign chairman Paul Manafort "breached" his plea agreement with the Justice Department by lying to the FBI and special counsel's office.

Following the allegations that Manafort lied to the special counsel, Trump said on Wednesday that he hadn't taken the possibility of pardoning his former campaign chairman off the table, telling the New York Post that "It was never discussed, but I wouldn't take it off the table. Why would I take it off the table?"

Additionally, Giuliani told CNN earlier this week that Manafort's legal team has been updating Trump's legal team with developments in the Mueller probe.

Giuliani on Thursday said he "wasn't briefed," and said there were two- to three minute conversations over the course of the last two months.

"Any extended conversation was after they voided the cooperation agreement," Giuliani said.

"I'm certain they were upset about it but I don't really care," Giuliani said about whether he was concerned if Mueller's team was upset about the two legal teams' communications. "They want to prosecute but don't want you to defend."

Giuliani also discussed the differences between Cohen and Manafort, as well as their involvement with the special counsel, calling the contrast between how the special counsel's team has treated the two men "unethical."

"They've reached a plea deal with a proven liar and (are) sending a signal to the world: If you tell us what you want to hear you get a nice big deal," Giuliani said of Cohen.