House Democrats on Monday raised the prospect of more articles of impeachment against President Trump, as Capitol Hill leaders hardened the impasse over a Senate trial on the two articles passed last week.

In a federal court battle over former White House Counsel Don McGahn’s refusal to testify before the impeachment inquiry, legal counsel for House Judiciary Committee Democrats argued the court needs to weigh in quickly, with a decision potentially affecting House Speaker Nancy Pelosi’s decision to send articles of impeachment to the Senate.

They also said more articles of impeachment were possible.

“McGahn’s testimony is also relevant to the committee’s ongoing investigations into presidential misconduct and consideration of whether to recommend additional articles of impeachment,” a committee lawyer wrote in a filing with the D.C. Court of Appeals.

The Justice Department, arguing for Mr. McGahn, said the courts should stay out of the impeachment fight that has becoming mired in partisan bickering.

The threat of more impeachment surfaced as Senate Majority Leader Mitch McConnell, Kentucky Republican, sparred with Democratic leaders from both chambers over how to conduct the trial.

He hit back at Mrs. Pelosi and Senate Minority Leader Charles E. Schumer for claiming his pro-Trump bias was cause to delay the trial.

“Do you think Chuck Schumer is impartial? Do you think Elizabeth Warren is impartial? Bernie Sanders is impartial? So let’s quit the charade. This is a political exercise,” he said on Fox News.

He later added, “I’m not anxious to have this trial, so if she wants to hang on to these papers, go right ahead.”

Mrs. Pelosi, California Democrat, put the brakes on sending the Senate two articles of impeachment that the House passed on a party-line vote last week. She said she didn’t trust the Republican-run chamber to conduct a fair trial.

Mr. Schumer, New York Democrat, is demanding new witnesses testify at the Senate trial. Republican leaders want to hear the House case before making that decision, which was the process followed in the impeachment trial of President Bill Clinton.

The stark partisan divide on impeachment all but assures Mr. Trump will be acquitted by the Senate, where it takes a two-thirds majority of the 100 senators to convict and remove a president from office.

Republicans charge that House Democrats rushed their case against Mr. Trump, deciding not to go to court to get documents and witnesses during the three-month impeachment inquiry. They say the executive branch is entitled to assert privileges, and it is up to the judiciary to settle that squabble.

Democrats accuse Mr. McConnell of trying to run a sham trial and being incapable of acting as an impartial juror because he is “in cahoots” with the White House.

The articles of impeachment charge Mr. Trump with abuse of power and obstruction of Congress. The abuse of power charge stems from Mr. Trump asking Ukraine to investigate former Vice President Joseph R. Biden, a leading candidate to oppose Mr. Trump in the 2020 general election. The second charge arises from Mr. Trump refusing to comply with subpoenas from the impeachment inquiry, which also is being litigated in federal court.

Mr. Trump shot back at Mrs. Pelosi — warning her that “breaking all the rules” will cost her the majority in 2020.

“Nancy Pelosi, who has already lost the House & Speakership once, & is about to lose it again, is doing everything she can to delay the zero Republican vote Articles of Impeachment,” he tweeted. “What right does Crazy Nancy have to hold up this Senate trial. None! She has a bad case and would rather not have a negative decision. This Witch Hunt must end NOW with a trial in the Senate, or let her default & lose. No more time should be wasted on this Impeachment Scam!”

However, Mr. Trump does find himself aligned with the Democrats in one way. They’d both like some witnesses to be called in to testify.

At a press conference in New York, Mr. Schumer reiterated his call for more documents and administration officials, such as White House Office of Management and Budget’s Michael Duffey. He cited newly released government emails that he said required more testimony about the decision to delay nearly $400 million of military aid to Ukraine.

One “explosive” record, in Mr. Schumer’s opinion, appears to link an OMB note to delay the military aid to Ukraine to the July 25 phone call between Mr. Trump and Ukrainian President Volodymyr Zelensky, which is at the heart of the impeachment case.

The OMB is denying that the email, though sent out about 90 minutes after the call, is linked to Mr. Trump’s request for an investigation of the Bidens, a request Mr. Zelensky did not flatly rule out during the phone call, though nothing eventually came of it and the aid was quickly released.

While those on the left are eyeing White House officials, the president would prefer witnesses such as Hunter Biden or House Intelligence Chairman Adam B. Schiff.

Mr. Trump’s request for an investigation focused on Hunter Biden, who got a lucrative job on the board of a Ukraine energy company while his father was leading Obama White House policy in that graft-riddled country.

Mr. Schiff, California Democrat, spearheaded the impeachment inquiry. His staff met with a whistleblower on the Ukraine call before he made the complaint to an inspector-general that launched the impeachment inquiry, prompting speculation that Mr. Schiff had orchestrated the whole thing.

Last week, Mr. McConnell and Senate Judiciary Chairman Lindsey Graham, South Carolina Republican, said they preferred to have a more streamlined proceeding rather than hear from new witnesses.

Mr. McConnell has maintained that the question of witnesses can be decided after opening arguments and written questions have been presented.

“We haven’t ruled out witnesses. We have said let’s handle it like we did with President [Bill] Clinton. Fair is fair,” he said. “We’re at an impasse. We can’t do anything until the speaker sends the papers over, so everybody enjoys the holidays.”

Mr. Schumer, who in 1998 supported the rule for the Clinton trial, would have none of it.

“We, at the very minimum, will require votes from all the senators on each of the witnesses and about each of these sets of documents, and I don’t think my colleagues — Democrat or Republican, are going to want to vote to withhold evidence,” he said.

• Jeff Mordock contributed to this report.

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