The use of cellular networks for massive machine-type communications (mMTC) is an appealing solution due to the wide availability of cellular infrastructure. Estimating the number of devices (network load) is vital for efficient allocation of the available resources, especially for managing the random access channel (RACH) of the network. This paper considers a two-priority RACH and proposes two network load estimators: a maximum likelihood (ML) estimator and a reduced complexity (RCML) variant. The estimators are based on a novel model of the random access behavior of the devices coupled with a flexible analytical framework to calculate the involved probabilities. Monte Carlo simulations demonstrate the accuracy of the proposed estimators for different network configurations.