Attempting to overturn election results in service of Donald Trump’s lie about voter fraud in his defeat by Joe Biden, the former New York mayor Rudy Giuliani told an Arizona official: “We’ve got lots of theories. We just don’t have the evidence.”

The Republican speaker of the Arizona house, Rusty Bowers, told the January 6 committee, “I don’t know if that was a gaffe. Or maybe he didn’t think through what he said. But both myself and … my counsel remember that specifically.”

For the committee, staging a fourth public hearing, the California Democrat Adam Schiff asked: “He wanted you to have the legislature dismiss the Biden electors and replace them with Trump electors on the basis of these theories of fraud?”

Bowers said: “He did not say in those exact words, but he did say that under Arizona law, according to what he understood, that would be allowed and that we needed to come into session to take care of that.”

This, Bowers said, “initiated a discussion about … what I can legally and not legally do. I can’t go into session in Arizona unilaterally or on my sole prerogative.”

In extensive questioning of his witness, Schiff asked if anyone at any time provided to Bowers “evidence of election fraud sufficient to affect the outcome of the presidential election in Arizona”.

Bowers said, “No one provided me ever such evidence.”

Biden won Arizona by about 10,000 votes, a margin slightly increased after a controversial review pursued by state Republicans.

Bowers told the hearing that Giuliani, other Trump aides and the 45th president himself made him think of The Gang That Couldn’t Shoot Straight, a classic novel of mob incompetence by the late New York journalist Jimmy Breslin.

“This is a tragic parody,” he said.

Bowers described harassment he and his family suffered. Another witness, Shaye Moss, a former Georgia elections worker, described threats and harassment dealt to her, her mother and her grandmother.

Schiff said: “Your proud service as an election worker took a dramatic turn on the day that Rudy Giuliani publicised video of you and your mother counting ballots on election night.”

Schiff played footage from a Georgia state senate hearing in which Giuliani said Moss and her mother were “quite obviously surreptitiously passing around USB ports as if they were vials of heroin or cocaine”.

Giuliani claimed it was “obvious to anyone who’s a criminal investigator or prosecutor, they are engaged in surreptitious illegal activity”, and said the women’s places of work and homes “should have been searched for evidence” of voter fraud.

What Giuliani said was a “USB port”, Moss said, was in fact “a ginger mint”.