WASHINGTON — The future of the House’s impeachment case against President Trump hung in doubt on Thursday, after the third-ranking House Democrat raised the possibility that the chamber could permanently withhold the articles from the Senate if it did not get assurances of a fair trial.

The morning after the House impeached Mr. Trump nearly along party lines, Representative James E. Clyburn, Democrat of South Carolina, said he was willing to wait “as long as it takes” to transmit the two impeachment articles approved Wednesday night. The House charged Mr. Trump with abuse of power and obstruction of Congress related to his campaign to pressure Ukraine to smear Democratic rivals.

“Until we can get some assurances from the majority leader that he is going to allow for a fair and impartial and trial to take place, we would be crazy to walk in there knowing he has set up a kangaroo court,” Mr. Clyburn said Thursday morning on CNN, referring to Senator Mitch McConnell, Republican of Kentucky and the majority leader.

His remarks came the morning after Speaker Nancy Pelosi threw the matter into doubt by telling reporters shortly after passage of the articles of impeachment that she might wait to transmit them to the Senate until she could determine whether the trial would be fair.

Pressed on whether Democrats should withhold the articles permanently, pulling the plug on a Senate trial, Mr. Clyburn said his personal preference would be to do so unless Mr. McConnell relents.

“If it were me, yes, that is what I am saying — I have no idea what the speaker would do,” Mr. Clyburn said. “If you have a preordained outcome that is negative to your actions, why walk into it? I would much rather not take that chance.”

Ms. Pelosi has indicated she will work with House chairmen and the Senate Democratic leader, Chuck Schumer of New York, to determine when the articles should be submitted and what meets her standard for fairness. In a news conference Wednesday night after the House votes, she said Mr. McConnell’s assertions that he would not be an impartial juror and would closely coordinate the trial with the White House left her in doubt that the House case would get a fair hearing.

She did not indicate that she was contemplating holding the articles forever.

Ms. Pelosi and Mr. Schumer were planning to meet later on Thursday morning to discuss their next steps.

While she did not say explicitly what she believes would constitute a fair trial, she indicated she would support the plan laid out by Mr. Schumer.

“We’d like to see a trial where it’s up to the senators to make their own decisions and working together, hopefully, in recognition of witnesses that the president withheld from us, the documents that president withheld from us,” Ms. Pelosi said.

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