Government funding actively engages in private R&D investment to enhance firm innovation. At the same time, firms are forced to find additional sources of competitive advantage, e.g., through cooperation based on the triple- or quadruple-helix principles. This paper analyses whether government funding and cooperation based on the triple-helix and quadruple-helix principles spur firms’ product and process innovation rather directly or indirectly, taking into account the role of firms R&D. For this purpose, we collect data from the Community Innovation Survey and analyse 5045 Norwegian firms by using partial least squares structural equation modelling. Our results confirm hypotheses that public funding and both triple-helix and quadruple-helix cooperation significantly influence firms’ research and development activities. Surprisingly, on the one hand, we showed that neither public funding nor triple- and quadruple-helix cooperation affect firms’ product innovation directly. Moreover, the results show a negative influence of government funding and triple- and quadruple-helix cooperation on Norwegian firms’ product innovation. On the other hand, process innovation is influenced positively and directly by firms’ cooperation based on the triple- and quadruple-helix principles. The results of our analyses clearly show the key role of firm’s R&D, which has proven to be a mediator of the effects of public funding and triple- and quadruple-helix cooperation on the product and process innovation activities of Norwegian firms.