Estimation of the direction-of-arrival (DOA) of sound sources is an important step in sound field analysis. Rigid spherical microphone arrays allow the calculation of a compact spherical harmonic representation of the sound field. The standard method for analyzing sound fields recorded using such arrays is steered response power (SRP) maps wherein the source DOA can be estimated as the steering direction that maximizes the output power of a maximally directive beam. This approach is computationally costly since it requires steering the beam in all possible directions. This paper presents an extension to SRP called steered response power density (SRPD) and an associated, signal-adaptive search method called hierarchical grid refinement for reducing the number of steering directions needed for DOA estimation. The proposed method can localize near-coherent as well as incoherent sources while jointly providing the number of prominent sources in the scene. It is shown to be robust to reverberation and additive white noise. An evaluation of the proposed method using simulations and real recordings under highly reverberant conditions as well as a comparison with the state-of-the-art methods are presented.