Oil rebounded by more than $1 to above $60 (39 pounds) a barrel on Tuesday as fighting in Libya, stronger equity markets and firm demand helped Brent futures recover from the biggest one-day loss in a month. Brent crude fell almost 5 percent on Monday as traders refocused on rising global supplies, which pushed oil prices down more than 60 percent between June and January. Oilfields and ports are increasingly a target in Libya’s conflict, which pits two rival governments and their armed forces against each other, nearly four years after the uprising that ousted leader Muammar Gaddafi.