Earlier Tuesday, White House spokesman Jay Carney referred questions on the appointment to the vice president's office.
In response to an inquiry from CNBC, a spokesperson for the vice president said, "Hunter Biden is a private citizen and a lawyer. The vice president does not endorse any particular company and has no involvement with this company."
A representative at Rosemont Seneca told CNBC that Biden was traveling and not immediately available for comment.
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Burisma touted Biden's "public service and foreign policy," and is listed as a co-founder of Rosement Seneca Partners, an investment advisory company. He also served as executive director of E-Commerce Policy Coordination under former Commerce Secretary William Daley, and co-chaired the 2008 Obama-Biden Inaugural Committee.
—By CNBC's Javier E. David.