what are you using for your sorce water if you are just using tap water then you are adding phos and other things that can feed the algae

also are you runing a sump or fuge of any kind if so get one started with macro algae as the macro will usualy outcompeet the ha if that is what it is

but I agree shut the lights off durring cycle no need to run them the algae die off will actualy help the cycle by creating dead material in the tank producing ammonia wich then processes through nitrite and nitrate

or can I use algea kill at this point?
dont waste your money on these products as they can quite often be very detrimental to a tank and also a lot of times contain copper wich will prevent you from beeing able to keep corals later on