The field of recommender systems has seen significant advancements recently, but several challenges remain. In this paper, we address two challenges in recommendation systems. Firstly, conventional recommendation systems require uploading private data to a central server for training, which inevitably impacts user privacy. To tackle this issue, we use Graph Federated Learning (GFL), a novel paradigm for distributed learning that ensures privacy preservation by enabling training on distributed data and eliminating direct data sharing. However, distributed recommender systems have a performance gap compared to non-distributed ones due to incomplete user-item interaction graphs. As a result, these systems struggle to utilize indirect user-item interactions effectively. Secondly, the cold start scenario, where a recommender system lacks sufficient data to make accurate recommendations for new users or items. Therefore, we propose MetaFRS - Federated Learning based Cold Start Recommendation System using Meta-Learning to overcome these limitations. Our system incorporates a graph neural network that uses attention mechanisms and an aggregation layer to summarize various orders of indirect user item and user-user interactions. Meta-learning algorithm is employed to address the issue of sparse interactions in cold start scenarios and incomplete user-item graphs in a distributed setup.