Rudy Giuliani, Donald Trump’s personal lawyer, has said he is confident the president will remain loyal to him as an impeachment inquiry unfolds in which the former New York mayor has become a central figure.

But Giuliani joked that he had good “insurance” in case Trump did turn on him, amid speculation Republicans will seek to frame him as a rogue actor.

In a telephone interview with the Guardian, in response to a question about whether he was nervous that Trump might “throw him under a bus” in the impeachment crisis, Giuliani said, with a slight laugh: “I’m not, but I do have very, very good insurance, so if he does, all my hospital bills will be paid.”

Giuliani’s lawyer, Robert Costello, who was also on the call, then interjected: “He’s joking.”

Whether it was a joke or a veiled threat, Giuliani has emerged as a key player in the impeachment proceedings, which center on the question of whether Trump sought to pressure the Ukrainian government to investigate his political rival, Joe Biden.

Testimony from diplomats in the lead-up to this week’s first public impeachment hearing has consistently pointed a finger of blame at Giuliani, who led the administration’s secret effort to pressure the Ukrainians to launch a corruption investigation into Biden’s son, Hunter.

In testimony, Bill Taylor, the top American diplomat in Ukraine, and George Kent, the deputy assistant secretary of state, have described how Trump seemed to care more about investigating Biden, his possible opponent in the 2020 election, than protecting a key ally from Russian aggression.

Taylor also described how one of his aides had heard a colleague, Gordon Sondland, the US ambassador to the EU, talking to Trump on the phone in July. The aide asked Sondland what Trump thought about Ukraine, and Sondland allegedly replied that Trump cared more about the investigations into Biden, which “Giuliani was pressing for”.

Giuliani told the Guardian he had no knowledge of the call, and made disparaging remarks about the case the Democrats had presented on the first day of the impeachment hearing.

“I’m not sure this is very solid testimony. In court we would call it hearsay, triple hearsay. It would not even be admissible. But if you are asking me flat out had I ever heard of a conversation like that? No,” he said.

“I thought it was a weak way to start a trial.”

Giuliani also defended his role as Trump’s attorney, and repeatedly said he had spoken to the president on Wednesday night, and that Trump had wished him a good night.

Asked about whether he believed Trump would remain loyal to him, amid speculation Republican lawmakers could seek to pin the blame for alleged wrongdoing on Giuliani personally in an effort to shield the president, Giuliani said he believed Trump, who he has known for three decades, was a “very loyal guy”.

“I acted properly as his lawyer,” Giuliani said. “I did what a good lawyer is supposed to do. I dug up evidence that helped to show the case against him was false; that there was a great deal of collusion going on someplace else other than Russia. And then I stepped on the number one minefield, which is Joe Biden, who is heavily protected by the Washington press corps.”

Sondland told Congress last month that Trump instructed his US diplomats to work through Giuliani to make it clear Ukraine’s access to the White House was contingent on their launching an investigation into his opponents.

The White House denounced the impeachment hearings as a “witch-hunt” and downplayed the serious corruption allegations.

Giuliani’s own ties to Ukraine date back to 2003. A Guardian investigation of his dealings in Ukraine, based on interviews with associates and business partners, showed Giuliani used his relationship with the president to gain access to high-ranking prosecutors and officials, and that his business associates traded on Giuliani’s name to seek to legitimize dubious business ventures.

Two of Giuliani’s business partners, Lev Parnas and Igor Fruman, helped to connect Giuliani to powerful Ukrainian prosecutors who claimed to have information about Hunter Biden, but also wanted to use Giuliani’s name to benefit their interests.

Parnas and Fruman, two Soviet-born Americans, were arrested on charges of violating campaign finance laws while attempting to travel to Vienna, shortly after they met Giuliani in Washington. Giuliani is also reportedly under investigation for whether his work in Ukraine broke laws on foreign lobbying.

Federal prosecutors are also reportedly investigating Giuliani for possible campaign finance violations and failure to register as a foreign agent, Bloomberg reported on Thursday.

The White House did not return a request for comment.