The House impeached Mr. Trump last week for abusing his power and obstructing Congress in connection with a campaign to pressure Ukraine to investigate his political rivals, including Mr. Biden and his son Hunter Biden. Since then, Speaker Nancy Pelosi of California has been in a standoff with Senator Mitch McConnell of Kentucky, the majority leader, over whether Democrats will be able to call Trump administration witnesses at a Senate trial.

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“I think Nancy Pelosi has done a remarkable job so far in a difficult situation,” Mr. Biden told reporters on his campaign bus later Friday. “I have confidence in her.”

But Mr. Trump and his Republican allies have sought to turn the tables by threatening to call Democrats, including the Bidens, to testify. That could allow Mr. Trump to amplify the same unfounded accusations against the Bidens that he was trying to get the Ukrainian president to agree to investigate in their July 25 phone call.

“We will have Schiff, the Bidens, Pelosi and many more testify, and will reveal, for the first time, how corrupt our system really is,” Mr. Trump tweeted this month before his impeachment, referring to Representative Adam B. Schiff of California, the chairman of the House Intelligence Committee.

The Senate, which is controlled by Republicans, could have difficulty calling Mr. Biden to testify, as some moderate party members might balk at the idea. The party holds 53 seats in the chamber and would need 51 votes to compel the former vice president to appear.

There is no evidence that the elder Mr. Biden, while serving as vice president, improperly intervened in Ukraine to benefit his son. But Hunter Biden was a board member of a Ukrainian energy company while his father worked on Ukraine policy under the Obama administration, a connection that some administration officials viewed as problematic.