Systematic reviews are fundamental to evidence-based medicine. Creating one is time-consuming and labour-intensive, mainly due to the need to screen, or assess, many studies for inclusion in the review. Several tools have been developed to streamline this process, mostly relying on traditional machine learning methods. Large language models (LLMs) have shown potential in further accelerating the screening process. However, no tool currently allows end users to directly leverage LLMs for screening or facilitates systematic and transparent usage of LLM-assisted screening methods. This paper introduces (i) an extensible framework for applying LLMs to systematic review tasks, particularly title and abstract screening, and (ii) a web-based interface for LLM-assisted screening. Together, these elements form AiReview-a novel platform for LLM-assisted systematic review creation. AiReview is the first of its kind to bridge the gap between cutting-edge LLM-assisted screening methods and those that create medical systematic reviews. The tool is available at https://aireview.ielab.io. The source code is also open sourced at https://github.com/ielab/ai-review.