An exploration of the dynamically generated Lambda and Sigma resonances has been made in the vector meson-baryon (VB) systems coupled to pseudoscalar meson-baryon (PB) channels. The VB interactions are obtained from the Lagrangians written within the hidden local symmetry which, in addition to Yukawa-type vector-baryon-baryon (VBB) vertices, naturally gives rise to a contact interaction. Using the VBB vertices, we calculate the t-, s-, and u-channel diagrams considering the octet baryon exchange in the latter two cases. For the PB channels we rely on the the Weinberg-Tomozawa interactions and calculate the PB <-> VB transition amplitudes extending the Kroll-Ruderman theorem by replacing the photon by the vector mesons. In addition to the low-lying Lambda(1405), Lambda(1670) found in previous works, we find resonances which coincide well with Lambda(2000), Sigma(1750)(S11), Sigma(1940)(D13), Sigma(2000)(S11) and predict three Lambda*'s with J(pi) = 3/2(-) and masses 1754 - i2 MeV, 1862 - i33 MeV, 2139 - i14 MeV together with a broad 1/2(-) Sigma* with mass similar to 1430 MeV. We find that most of these next-to-low-lying states couple weakly with the pseudoscalar mesons, which implies that it is important to study the reactions with VB final states in order to obtain reliable information on the properties of such resonances.