We consider the verification of current-state and K-step opacity for systems modeled as interacting nondeterministic finite-state automata. We describe a new methodology for compositional opacity verification that employs abstraction, in the form of a notion called opaque observation equivalence, and that leverages existing compositional nonblocking verification algorithms. The compositional approach is based on a transformation of the system, where the transformed system is nonblocking if and only if the original one is current-state opaque. Furthermore, we prove that K-step opacity can also be inferred if the transformed system is nonblocking. We provide experimental results where current-state opacity is verified efficiently for a large scaled-up system.