This position paper provides a statement on the criticality of research software in artificial intelligence (AI)-driven research and makes recommendations for stakeholders on how to consider research software in their AI goals and incorporate it in their AI activities. This paper discusses both research software that supports generative AI, which is now being explored today as a tool to enable new research, as well as more traditional machine learning, which has already demonstrated impact in research in most disciplines. The fact that AI is dependent on software (i.e., data preparation and model training are performed by software, models are implemented in software) is not always adequately considered, nor are the challenges inherent in software dependencies. Recognising this is needed to ensure that the focus on technological infrastructure to support AI acceleration includes research software and its personnel as a vital part of that infrastructure. The paper also explores a need to better support the people who develop and maintain the research software that enables AI-driven research; illustrates how some countries are operationalising AI strategies that could support the critical element of research software (e.g., by building on existing investments in research software); and provides a list of recommendations for research software to support AI, organised in three areas from the Amsterdam Declaration on Funding Research Software Sustainability: research software practice, research software ecosystem, and research software personnel.