BAT's cash-and-stock offer would mark the return of the company to the lucrative and highly regulated U.S. market after a 12-year absence, making it the only tobacco giant with a leading presence in the American and international markets.
Some analysts have predicted that the deal could encourage current market leader Philip Morris International to reunite with its U.S. affiliate Altria, reversing a 2008 spin-off of the international business.
Both Reynolds American and BAT declined to comment.
Bloomberg was the first to report on Reynolds' rejection.
Reynolds American had a market capitalization of about $76 billion as of Monday's close of $53.05. The company's stock had risen nearly 15 percent this year.