Bucking pressure from businesses and fellow lawmakers, Sen. Rand Paul says he will continue to oppose tax treaties that would let the Internal Revenue Service gather more information about Americans’ overseas financial accounts.

The move dims the outlook for a planned Senate vote on the treaties, while highlighting the Kentucky Republican’s contrarian streak. The treaties – including a significant one with Switzerland – enjoy widespread support among lawmakers of both parties. But Mr. Paul, who is preparing a 2016 presidential bid, believes they would encourage government snooping and erode Americans’ privacy rights.