ROCHESTER, N.H.—Former Vice President Joe Biden said Wednesday for the first time that President Trump should be impeached, telling supporters in New Hampshire that the president had “violated his oath of office.”

Mr. Biden, who had previously stopped short of calling for outright impeachment, offered a forceful rationale in urging Congress to impeach his presidential rival. He said Mr. Trump had obstructed justice by refusing to comply with congressional inquiries and committed impeachable acts in plain sight.

“In...