Respiratory epithelial cells and macrophages are the key innate immune cells that play an important role in the pathogenesis of influenza A infection. We found that these two cell types from both human and pig showed comparable susceptibility to initial infection with a highly pathogenic avian influenza (HPAI) H5N1 (A/turkey/Turkey/1/05) and a moderately pathogenic human influenza H1N1 (A/USSR/77) virus, but there were contrasting differences in host innate immune response. Human cells mounted vigorous cytokine (TNF-α and IL6), and chemokine (CXCL9, CXCL10 and CXCL11) responses to H5N1 virus infection. However, pig epithelial cells and macrophages showed weak or no TNF-α and chemokine induction to the same infections. The apparent lack of a strong pro-inflammatory response, corroborated by the absence of TNF-α induction in H5N1 virus challenged pigs, coincided with greater cell death and reduced release of infectious virus from infected pig epithelial cells. Suppressor of cytokine signalling 3 (SOC3), a protein suppressor of the JAK-STAT pathway, was constitutively highly expressed and transcriptionally up-regulated in H5N1 virus infected pig epithelial cells and macrophages in contrast to corresponding human cells. Over-expression of SOCS3 in infected human macrophages dampened TNF-α induction. In summary, we found that reported low susceptibility of pigs to contemporary Eurasian HPAI H5N1 virus infections coincides at the level of innate immunity of respiratory epithelial cells and macrophages with reduced viable virus output and an attenuated pro-inflammatory response, possibly mediated in part by SOCS3 which could serve as a target in the treatment or prevention of virus-induced hypercytokinemia as observed in humans.