assume its a close coupled unit. ie cistern sits on toilet pan.
if you seen slow run of water into pan it could be caused by
1.Syphon securing nut loose so slowly draining in to toilet bowl.
2. Fault with syphon continuing to slowly syphon water as it fills.
Turn off the water to cistern remove the connection pipe. Remove any water from cistern.
Remove wall fixing screws from rear of cistern (inside)
Remove the cistern to toilet pan securing nuts
Lift cistern clear of toilet. check the nut and its washer which secures the syphon to the cistern if loose that is most likely the cause if not replace the syphon which may be faulty.
In any case you have to replace the rubber seal between pan and cistern buy as kit plate and seal.
I base this on that you don't mention finding water on the floor. If its the low level with flush tube from cistern to toilet then most likely faulty syphon replace it. If floor wet tighten flush tube nut under cistern.
Trail and error with this fault.
bob
December 2011