Achieving sustainable and inclusive development remains one of the most pressing objectives for advanced societies. In this context, universities and public research institutions have become key players, not only in producing knowledge, but in shaping the ways in which that knowledge responds to global challenges. The Sustainable Development Goals (SDGs), particularly those related to inclusive economic growth (SDG 8), infrastructure and innovation (SDG 9), and climate action (SDG 13), require a shift in how institutions operate and innovate (Picatoste et al., Int J Sustain Higher Educ, 2024). There is growing social demand for organisations to not just contribute to economic performance, but to do so responsibly, ethically, and equitably (Leal Filho et al., Sustainability, 12(9):3761, 2020; Dhamija and Bag, TQM J, 32(4):869–896, 2020). This paper takes a closer look at how public universities help advance these goals, especially through the development of responsible artificial intelligence (AI). The analysis focuses on one approach, green algorithms, which seek to reduce the environmental impact of AI systems. While these technologies have gained attention, their potential to contribute to economic and environmental sustainability is still underexplored. The aim here is to bridge that gap, offering a multidisciplinary analysis that draws from economics, sustainability science, and digital innovation. In doing so, the article hopes to offer insights not just for academia, but for public policy and organizational strategies moving toward a greener AI future.