A key ally of President Biden floated the idea of a “mini-primary” to replace Mr. Biden at the top of the Democratic ticket.

Rep. James Clyburn, South Carolina Democrat, noted Wednesday that the party already plans a virtual roll call ahead of the nominating convention to jump through a legal hoop in Ohio and get Mr. Biden’s name on the ballot in that state.

The former chairman of the Congressional Black Caucus said that meeting could become the “mini-primary,” and he would support that if the president suspends his campaign.

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“You can actually fashion the process that’s already in place to make it a mini primary, and I would support that absolutely,” Mr. Clyburn said in a CNN interview. “We can’t close that down, and we should open up everything for the general election.”

Top-level Democrats have rallied around Mr. Biden and only two elected Washington Democrats have publicly called for Mr. Biden to step aside in the wake of last week’s dismal debate performance.

Administration officials, reports of Mr. Biden’s words in private, and White House responses to news reports, all have been emphatic in denying any possibility of his dropping out or the existence of plans to do so.

Mr. Clyburn has publicly said he supports the president and his spokeswoman told Politico that her boss’s CNN interview did not indicate any preparation for a Plan B.

“It is quite obvious that Congressman Clyburn was responding to a hypothetical question,” Brianna Frias told Politico. “He was not calling for a ‘mini primary.’ Instead, he was explaining the existing process. The Congressman fully supports President Biden at the top of the ticket and it would be irresponsible to report anything otherwise.”

Still, Mr. Clyburn did further muse in Wednesday’s CNN interview about the possibility of a contested primary and noted the uncommitted status of hundreds of “superdelegates” — mostly Democratic elected officials unplugged to vote for any candidate.

“It would seem to me that any one of these people who aspire to be president, who would like to see a contest taking place — look at those 700 delegates who are now uncommitted and get into the action,” he said.

Mr. Clyburn was influential in making Mr. Biden president in the first place.

His endorsement of Mr. Biden before the 2020 South Carolina primary is widely credited with sealing a big victory for Mr. Biden in the third state to vote.

That win let Mr. Biden recover from disappointing finishes in both Iowa (fourth) and New Hampshire (fifth) and he went on to secure the Democratic nomination.