We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space R3 . When the small rigid body shrinks to a point in the sense that its density is constant, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier–Stokes equations in the full space.Based on some $L^p$-$L^q$ estimates of the fluid–structure semigroup and a fixed point argument, we obtain a uniform estimate of velocity of the rigid body. This allows us to construct admissible test functions which plays a key role in the procedure of passing to the limit.