Washington (CNN) President Donald Trump continues to speak with his personal attorney Rudy Giuliani on the phone, according to multiple people with knowledge, as the ongoing impeachment inquiry has accelerated. Those people say the men's attorney-client relationship remains close even as Giuliani's central role in the series of events leading to the start of the congressional probe becomes increasingly apparent.

"Rudy is uniquely the President's peer of all the people who work in the legal side," said one person with knowledge of their relationship.

But Giuliani has also withdrawn from his prominent public role as a defender of the President in the media after he himself came under scrutiny for his efforts to shape US policy toward Ukraine. Those activities have drawn the attention of federal prosecutors in Manhattan, and Giuliani announced earlier this week he has hired his own legal team.

Giuliani, who has said he represents Trump pro bono, confirmed to CNN Thursday he remains on the President's legal team.

"I am honored to be part of the team committed to defending President Trump against this phony claim ... being carried out by craven Democrats on Capitol Hill. It is a disgrace to our democracy," said Giuliani in a statement emailed by his assistant.

Asked how often he and Trump still speak, Giuliani said, "How often myself and President Trump communicate is entirely privileged."

The last known face-to-face meeting Trump had with Giuliani was on October 12, when they met for lunch at Trump's golf course in Virginia. One person close to the White House said their discussion was friendly and focused primarily on politics.

One person familiar said as recently as late October, Trump called Giuliani about once a day. Another person familiar said the President enjoys Giuliani's company and discusses topics beyond legal issues with him.

The 'Giuliani factor'

But developments in the impeachment inquiry risk straining the close relationship between Trump and Giuliani as it becomes more clear how Giuliani's shadow foreign-policy operation with Ukraine has put his most famous client in political danger.

The initial whistleblower complaint cited Giuliani's influence on Ukraine policy as a prominent concern. And witness testimony released this week by House Democrats has further confirmed the former New York City mayor's role in the series of events surrounding the temporary hold on US military aid.

Gordon Sondland, the US ambassador to the European Union and one of the witnesses whose testimony was released this week, told lawmakers Trump had directed administration officials to treat Giuliani as a point person on matters involving Ukraine.

"He just kept saying: Talk to Rudy, talk to Rudy," Sondland testifed.

The former special envoy to Ukraine, Kurt Volker, testified about what he called the "Giuliani factor" -- that is, the way Giuliani often colored Trump's views of Ukraine and its new president, Volodymyr Zelensky, that would be at odds with the administration's official diplomatic efforts.

"The negative narrative which Mr. Giuliani was furthering was the problem ... it was impeding our ability to build the relationship the way we should be doing," Volker told lawmakers.

And testimony from George Kent , a career foreign service officer serving as the deputy assistant secretary for European and Eurasian affairs, demonstrates the extent to which administration officials viewed Giuliani's influence on Trump's views on Ukraine as a problem.

Kent called Giuliani's public and private efforts to push the new Ukrainian government to announce criminal investigations that would benefit Trump politically a "campaign of lies."

Kent also described the effects of the Giuliani factor on other officials, including the "freelancing" Sondland, causing concern within the State Department that the President's personal attorney was facilitating a run-around on the official processes of US foreign policy.

'A little rough around the edges'

Republican members of Congress have expressed unease at Giuliani's role in the Ukraine saga. And a person close to Trump says the President knows Giuliani is a partial liability. But this person reiterated that Trump does not cut people loose at the first sign of trouble. An October 12 tweet from Trump summed up this view.

"He may seem a little rough around the edges sometimes, but he is also a great guy and wonderful lawyer," the President wrote.

The most recent time Trump mentioned Giuliani in public was October 30, when he told reporters on the South Lawn of the White House that his lawyer was a "good man."

"I think Rudy Giuliani is a great crime fighter. He was the greatest mayor in New York City history, but he has been a great crime fighter. He's always looking for corruption, which is what more people should be doing," Trump said.

Trump's loyalty to Giuliani traces back to their similar backgrounds and years of friendship. They rose to prominence together in 1980s and 90s New York, supported each other's political endeavors and -- when they failed -- offered consolation (Giuliani has said he spent a month at Trump's Mar-a-Lago estate after an ill-fated presidential run in 2008).

And their bond was bolstered after the release of the "Access Hollywood" tape weeks before the 2016 election. Giuliani remained a public attack dog on Trump's behalf, something the person close to Trump identified as an important moment for solidifying the President's confidence in him. For the President, Giuliani's value is less his legal advice than his willingness to ferociously defend him on television.

But Giuliani has undoubtedly retreated from the public eye in recent weeks as the scrutiny has turned to him. His last TV interview was October 9 on Fox News, the same day two associates who helped Giuliani connect with Ukrainian officials, Lev Parnas and Igor Fruman, were arrested and later indicted on federal charges of money laundering. He also appears to have spoken less frequently with reporters since then.

Giuliani's Twitter feed, however, has remained active. On Thursday, for instance, Giuliani defended himself and Trump.

"The evidence, when revealed fully, will show that this present farce is as much a frame-up and hoax as Russian collusion, maybe worse, and will prove the President is innocent," he wrote