This paper deals with the generalization of usual round spheres in the flat Minkowski spacetime to the case of a generic four-dimensional spacetime manifold M. We consider geometric properties of sphere-like submanifolds in M and impose conditions on its extrinsic geometry, which lead to a definition of a rigid sphere. The main result is a local existence theorem concerning such spheres. For this purpose, we apply the surjective implicit function theorem. The proof is based on a detailed analysis of the linearized problem and leads to an eight-parameter family of solutions in case when the metric tensor g of M is from a certain neighborhood of the flat Minkowski metric. This contribution continues the study of rigid spheres in (Class. Quantum Grav. 30: 175010, 2013).