The New York Republican congressman George Santos, whose résumé has been shown to be largely fictional, whose campaign finances are the subject of increasing scrutiny and who is under local, federal and international investigation, is a “bad guy” who has done “really bad” things, the new House oversight committee chairman said on Sunday.

But Santos should not be forced to quit, James Comer said.

“He’s a bad guy,” the Kentuckian told CNN’ State of the Union. “This is something that you know, it’s really bad … but look, George Santos was a duly elected by the people. He’s going to be … examined thoroughly. It’s his decision whether or not he should resign.”

Saying Santos was “not the first politician unfortunately to be in Congress to lie”, Comer said he had not introduced himself to Santos, “because it’s pretty despicable the lies that he told”. But he said only proven campaign finance violations should lead to Santos’s removal.

Santos was going to be investigated, Comer said, “not necessarily for lies but for potential campaign finance violations … It’s his decision whether or not he should resign.”

Santos won New York’s third district, which covers parts of Long Island and Queens, in November. Since then his biography has been shown to be largely made-up and his campaign finances scrutinised amid questions about his personal wealth.

This week, Democrats in Congress requested an ethics committee campaign finance investigation and a nonpartisan watchdog, the Campaign Legal Center, filed its own request for an investigation by the Federal Election Commission.

The CLC complaint said: “Particularly in light of Santos’s mountain of lies about his life and qualifications for office, the [FEC] should thoroughly investigate what appear to be equally brazen lies about how his campaign raised and spent money.”

Santos’s district party has disowned him and New York Republicans in Congress have called on him to resign. Santos has said he will not.

Kevin McCarthy, the House speaker who Santos supported through 15 rounds of voting earlier this month, and who must operate with a small majority, has not taken action, instead pointing to a House ethics office his party is attempting to gut.

On Sunday Don Bacon of Nebraska, a Republican moderate, told ABC’s This Week: “You know, if that was me, I would resign. I wouldn’t be able to face my voters.”

But Bacon still followed the party line: “This is between him and his constituents, largely. They’ve elected him and they have to deal with him on that. I don’t think his re-election chances would be that promising.”

One of the Democrats who demanded an investigation said he had written to McCarthy and other senior Republicans.

Dan Goldman, also of New York, told CBS’s Face the Nation: “The speaker of the House indicated that he would support an ethics investigation.

“And in fact this morning, Congressman [Ritchie] Torres and I sent a letter to Speaker McCarthy, [Republican] chairwoman [Elise] Stefanik and the head of the Congressional Leadership Fund, Kevin McCarthy’s super Pac, because there’s really, really bombshell … reporting from the New York Times that they all knew about Mr Santos’s lies prior to the election.”

Goldman said he and Torres were calling on Republicans “to be fully cooperative with the investigators, both in Congress and outside of Congress to disclose exactly what they knew about Mr Santos’s lies, and whether they were complicit in this scheme to defraud voters.

“George Santos is a complete and total fraud … nearly everything has proven to be a lie. His financial disclosures have clear false statements and omissions. And that’s what we refer to the ethics committee for an investigation to get to the bottom of whether he broke the law.

“Eight Republican Congress members have called on him to resign … This is a scheme to defraud the voters of the third district in New York, and this needs to be investigated intensively. And Mr Santos needs to think twice about whether he belongs in Congress. And more importantly, the speaker needs to think twice about whether Mr Santos is fit to serve in Congress.”

On Saturday, a prominent GOP right-winger – and ringleader of the attempt to stop McCarthy becoming speaker – offered Santos support.

Speaking to CNN, Matt Gaetz of Florida said: “George Santos represents over 700,000 people in New York. And whether people like that or not, those people deserve to have members of Congress collaborating with the person who serves them.

“George Santos will have to go through the congressional ethics process. I don’t want to prejudge that process, but I think he deserves the chance to at least make his case.”

Earlier this week, Gaetz spoke to Santos on the former Trump adviser Steve Bannon’s podcast. Asked about his wealth, Santos nodded to Republican claims about Hunter Biden, Joe Biden’s son, saying: “I’ll tell you where it didn’t come from – it didn’t come from China, Ukraine or Burisma.”

Santos is under investigation in Brazil, over the use of a stolen chequebook, and in the US over claims about his college history, business career and family background shown to be untrue. Santos has admitted “embellishing” his résumé but insisted he has done nothing wrong or unethical.

On Bannon’s podcast, Gaetz said: “Embellishing one’s résumé isn’t a crime. It’s frankly, how a lot of people get to Congress. And we want everyone to be honest.”

Writing for the Guardian, the columnist Moira Donegan pointed to Santos’s rise in a Republican party led by Donald Trump.

“It would be a mistake to think that George Santos’s pathologies are his alone,” she wrote. “His lies are the product of a political system that incentivises dishonesty, punishes sincerity and is rife with opportunities for petty crooks.

“In that sense, Santos is the politician that we deserve.”