In this second paper of the series on internal gravity waves ( IGWs ) , we present a study of the generation and propagation of IGWs in a model solar atmosphere with diverse magnetic conditions . A magnetic field free , and three magnetic models that start with an initial , vertical , homogeneous field of 10 G , 50 G , and 100 G magnetic flux density , are simulated using the CO ^ { 5 } BOLD code . We find that the IGWs are generated in similar manner in all four models in spite of the differences in the magnetic environment . The mechanical energy carried by IGWs is significantly larger than that of the acoustic waves in the lower part of the atmosphere , making them an important component of the total wave energy budget . The mechanical energy flux ( 10 ^ { 6 } –10 ^ { 3 } W m ^ { -2 } ) is few orders of magnitude larger than the Poynting flux ( 10 ^ { 3 } –10 ^ { 1 } W m ^ { -2 } ) . The Poynting fluxes show a downward component in the frequency range corresponding to the IGWs , which confirm that these waves do not propagate upwards in the atmosphere when the fields are predominantly vertical and strong . We conclude that , in the upper photosphere , the propagation properties of IGWs depend on the average magnetic field strength and therefore these waves can be potential candidate for magnetic field diagnostics of these layers . However , their subsequent coupling to Alfvénic waves are unlikely in a magnetic environment permeated with predominantly vertical fields and therefore they may not directly or indirectly contribute to the heating of layers above plasma- \beta less than 1 .