We present a theoretical study of the creep rupture of heterogeneous materials based on a fiber bundle model which provides a direct connection between the microscopic fracture mechanisms and the macroscopic time evolution. In the model, material elements fail either due to immediate breaking or undergo a damage accumulating ageing process. We found that on the micro-level the competition of the two failure modes gives rise to bursts of breakings with power law distributed size and waiting time between events. We demonstrate that approaching macroscopic failure the system accelerates which can be fully described as a non-homogeneous Poissonian process for long range load sharing, however, when localization occurs breaking events get clustered. Bursts are composed of sub-avalanches which lead to a non-trivial temporal shape comparable to measurements. The pulse shape proved to be sensitive to the range of load sharing.