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We obtain asymptotic equalities for least upper bounds of deviations in theuniform metric of de la Vall\'{e}e Poussin sums on the setsC^{q}_{\beta}H_\omega of Poisson integrals of functions from the class H_\omegagenerated by convex upwards moduli of continuity \omega(t) which satisfy thecondition \omega(t)/t\to\infty as t\to 0. As an implication, a solution of theKolmogorov-Nikol'skii problem for de la Vall\'{e}e Poussin sums on the sets ofPoisson integrals of functions belonging to Lipschitz classes H^\alpha,0<\alpha <1, is obtained

Uniform approximation of Poisson integrals of functions from the class H_omega by de la Vallee Poussin sums