Before establishing a communication link in a cellular network, the user terminal must activate a synchronization procedure called initial cell search in order to acquire specific information about the serving base station. To accomplish this task, the primary synchronization signal (PSS) and secondary synchronization signal (SSS) are periodically transmitted in the downlink of a Long Term Evolution (LTE) network. Since SSS detection can be performed only after successful identification of the primary signal, in this work we present a robust scheme for joint PSS detection, sector index identification and integer frequency offset (IFO) recovery in an LTE system. The proposed algorithm relies on the maximum likelihood (ML) estimation criterion and exploits a suitable reduced-rank representation of the channel frequency response to take multipath distortions into account. We show that some PSS detection methods that were originally introduced through heuristic reasoning can be derived from our ML framework by selecting an appropriate model for the channel gains over the PSS subcarriers. Numerical simulations indicate that the proposed scheme can be effectively applied in the presence of severe multipath propagation, where existing alternatives provide unsatisfactory performance.