“Hunter Biden is a private citizen and a lawyer,” she said. “The vice president does not endorse any particular company and has no involvement with this company. The vice president has pushed aggressively for years, both publicly with groups like the U.S.-Ukraine Business Forum and privately in meetings with Ukrainian leaders, for Ukraine to make every effort to investigate and prosecute corruption in accordance with the rule of law. It will once again be a key focus during his trip this week.”

Ryan F. Toohey, a Burisma spokesman, said that Hunter Biden would not comment for this article.

It is not known how Mr. Biden came to the attention of the company. Announcing his appointment to the board, Alan Apter, a former Morgan Stanley investment banker who is chairman of Burisma, said, “The company’s strategy is aimed at the strongest concentration of professional staff and the introduction of best corporate practices, and we’re delighted that Mr. Biden is joining us to help us achieve these goals.”

Joining the board at the same time was one of Mr. Biden’s American business partners, Devon Archer. Both are involved with Rosemont Seneca Partners, an American investment firm with offices in Washington.

Mr. Biden is the younger of the vice president’s two sons. His brother, Beau, died of brain cancer in May. In the past, Hunter Biden attracted an unusual level of scrutiny and even controversy. In 2014, he was discharged from the Navy Reserve after testing positive for cocaine use. He received a commission as an ensign in 2013, and he served as a public affairs officer.

Before his father was vice president, Mr. Biden also briefly served as president of a hedge fund group, Paradigm Companies, in which he was involved with one of his uncles, James Biden, the vice president’s brother. That deal went sour amid lawsuits in 2007 and 2008 involving the Bidens and an erstwhile business partner. Mr. Biden, a graduate of Georgetown University and Yale Law School, also worked as a lobbyist before his father became vice president.