Rudy Giuliani, President Trump's personal lawyer, criticized the timing of Michael Cohen's guilty plea on charges of lying to Congress: just before the president was about to leave for a high-stakes G-20 summit in Argentina.

Giuliani issued a statement Thursday saying Mueller's office was proving Trump's former lawyer lied to Congress by using documents that were already voluntarily disclosed by the Trump Organization "because there was nothing to hide."

"It is hardly coincidental that the Special Counsel once again files a charge just as the President is leaving for a meeting with world leaders at the G20 Summit in Argentina," Giuliani said.

Giuliani's statement called out Mueller's office for playing politics with the surprise announcement. Giuliani pointed to a similar decision in July when the Department of Justice announced that 12 Russian intelligence officers were to be indicted for allegedly hacking the Democratic National Committee and others.

The July indictment was announced days before Trump was slated to hold a key summit with Russian President Vladimir Putin in Helsinki. Trump was meeting with Queen Elizabeth II in Britain at the time of the announcement.

Politico spoke to White House officials who hoped the G-20 summit would showcase Trump's ability to negotiate. Trump's upcoming Saturday lunch with China's President Xi Jinping is seen by some to be a make-or-break meeting between the two leaders. Trump also called off a meeting with Putin over the recent naval clash with Ukraine.

Cohen confessed in a surprise guilty plea Thursday that he lied to Congress about a Moscow real estate deal he pursued on Trump’s behalf during the heat of the 2016 campaign for the Republican presidential nomination. He said he lied to be consistent with Trump’s "political messaging."

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The agreement made clear that prosecutors believe Trump's former lawyer was continuing to pursue the Trump Tower Moscow project weeks after his boss had clinched the Republican nomination for president and well after the point that Cohen has publicly acknowledged.

According to a report by BuzzFeed News, Trump’s company planned to give the tower's penthouse to Putin as they worked on a real estate deal for the building during the 2016 campaign. The claim was sourced by four people, including one of the plan’s creators.

But the plan would have been a “stupid idea,” the source told Fox News on Thursday night, adding that the president “never heard of it.”

Fox News is told Trump's legal team was unaware of such a plan.

Plans for constructing the building were ultimately scrapped.

There is no clear link in the court filings between Cohen’s lies and Mueller’s central question of whether the Trump campaign colluded with Russia. And nothing said in court, or in associated court filings, addressed whether Trump or his aides had directed Cohen to mislead Congress.

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

Fox News' Matt Richardson and Brooke Singman and the Associated Press contributed to this report.