We report new searches for solar axions and galactic axionlike dark matter particles, using the first low-background data from the PandaX-II experiment at China Jinping Underground Laboratory, corresponding to a total exposure of about 2.7×10^{4} kg day. No solar axion or galactic axionlike dark matter particle candidate has been identified. The upper limit on the axion-electron coupling (g_{Ae}) from the solar flux is found to be about 4.35×10^{-12} in the mass range from 10^{-5} to 1 keV/c^{2} with 90% confidence level, similar to the recent LUX result. We also report a new best limit from the ^{57}Fe deexcitation. On the other hand, the upper limit from the galactic axions is on the order of 10^{-13} in the mass range from 1 to 10 keV/c^{2} with 90% confidence level, slightly improved compared with the LUX.