The low-lying light tetraquark states are investigated in the nonrelativistic quark model including the pseudoscalar meson exchange, where two different confinement potential schemes, the Cornell potential and the linear potential, are employed, along with the instanton-induced interaction serving as the residual spin-dependent interaction. The numerical results show agreement with masses of , , , , , , , , , , , , , , , , , , , , , , , , , , and . The results shed light on the spectrum of these mesons and offer guidance to search for the tetraquarks in the future.