Former President Donald J. Trump’s full takeover of the Republican National Committee continued this week with interviews for key positions that have included a jarring question: Was the 2020 presidential election stolen?

That question has been asked in interviews aimed at replacing some of the more than 60 R.N.C. officials who were laid off this month, according to two people familiar with the matter.

Most of the applicants who were posed the question responded with some version of an answer saying that there had been irregularities in the 2020 presidential contest and that changes to rules and laws that year because of the coronavirus pandemic had created cause for concern, the people familiar with the matter said. There is no evidence of widespread fraud in that year’s election, but Mr. Trump and some of his allies have continued to cast doubt on its legitimacy.

The Washington Post first reported that the R.N.C. interviews included a question about the validity of the 2020 election.

It was unclear how the answers from applicants would affect party officials’ hiring decisions. An R.N.C. spokeswoman did not immediately respond to a request for comment.

This month, the R.N.C. elected new leaders who were handpicked by Mr. Trump, including his daughter-in-law, Lara Trump.

For the past several years, R.N.C. lawyers have instructed party officials to avoid claiming that widespread fraud altered the outcome of the 2020 presidential election, or that the contest was stolen. Instead, the lawyers have urged officials to say that some states had eliminated voting safeguards and to underscore a need for poll watchers.

Those warnings about careful language came as multiple Trump advisers faced criminal charges for their role in trying to overturn the 2020 election.

Top R.N.C. officials were also worried about making false election claims given that the party had only recently been released from a decades-long ban on mounting campaigns against purported voter fraud without court approval. That ban, which was lifted by a 2018 federal court ruling, was first imposed in 1982 after courts found instances of Republicans intimidating or trying to exclude voters of color.

President Biden’s campaign immediately jumped on reports about the R.N.C. interview question.

“Donald Trump is demanding fealty to his extreme, antidemocratic beliefs to be part of his Republican Party,” Ammar Moussa, a campaign spokesman, said in a statement. “Americans don’t want his lies, attacks on democracy, calls for violence or dangerous agenda.”