Hunter Biden, the president’s son, surprised Republicans on the House Oversight Committee on Wednesday morning when he briefly appeared in the hearing room as they were poised to vote to hold him in contempt of Congress for failing to sit for a private deposition.

The arrival of the younger Mr. Biden, who has repeatedly offered to testify publicly in the impeachment inquiry into President Biden but refused to be interviewed behind closed doors, prompted chaos in the proceedings as Democrats and Republicans bickered about whether to allow him to be heard.

The exchange pitted some of the staunchest supporters of former President Donald J. Trump against the son of his successor and chief political rival, underscoring the bitter polarization that is driving the impeachment investigation.

Democrats on the panel urged the Republicans who control it to let Mr. Biden testify right then and there, but G.O.P. lawmakers insisted he must submit to a closed-door deposition as ordered by their subpoena.

As Representative Marjorie Taylor Greene, Republican of Georgia, was beginning to speak against the younger Mr. Biden, he and his entourage left the room just minutes after arriving, which prompted Ms. Greene to label him a “coward.”

“Hunter Biden is terrified of strong conservative Republican women because he can’t even face my words,” said Ms. Greene, who had displayed nude photos of Mr. Biden during a previous committee hearing.