Where can I get threads compatible with LEGO pulleys? Have LEGO threads ever been produced? Even the biggest LEGO rubber band is too short to meet my requirements. 

I need them for this year's WRO challenge. Note that the challenge only allows Lego products, so I can't just buy the rubber band I need elsewhere.
There are many kinds of LEGO string, which are compatible with pulleys, but they are not closed in a loop, but manufactured as a single thread. You could tie a knot on them to form a loop, but the string lacks the traction of a rubber band, so you should definitely consider this if you plan to transmit power via a belt drive made of a string.