The gunman reportedly dressed as Santa Claus shot dead a policeman and a civilian at the entrance to the Reina nightclub, one of the city's most exclusive party venues, before going on a shooting rampage inside, according to the authorities.
NTV television said many party-goers threw themselves into the Bosphorus in panic after the attack and efforts were under way to rescue them from the waters.
"The United States condemns in the strongest terms the horrific terrorist attack at a nightclub in Istanbul, Turkey, which has left dozens dead and many more wounded," National Security Council spokesman Ned Price said in a statement.
Price added: "We reaffirm the support of the United States for Turkey, our NATO ally, in our shared determination to confront and defeat all forms of terrorism.