To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU(N) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU(N) Neel and valence-bond solid phases is characterized for N = 2, 3, and 4 on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size (L = 256) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent y equivalent to 1/nu as the system size increases. We also confirm the relevance of a squared valence-bond solid field Psi(2) for the SU(3) model.