Federated learning is a machine learning paradigm that enables collaborative model training across decentralized datasets while preserving data privacy. By allowing diverse institutions, such as hospitals and clinical laboratories, to contribute data without sharing it, this approach facilitates the development of improved models. Sensitive information remains protected as data resides on the originating devices, addressing critical privacy concerns inherent in traditional centralized learning methodologies. This paper addresses instrument segmentation during Minimally Invasive Surgeries (MIS) using a federated learning approach. Centralized learning from different hospital departments or institutions is often hindered by data silos and privacy constraints. The aim here is to derive a generalized model from distributed datasets with varied annotations related to MIS procedures. A horizontal federated learning method is tailored for the Endovis 2017 Dataset, encompassing three distinct annotation types representing binary (detect the presence of the instrument), type (different types of instruments), and parts (different parts of the same instrument) intended segmentation tasks. To address the inherent data variability in surgical instrument segmentation, we propose an adaptive aggregation strategy to overcome the challenges posed by non-IID data distribution. This approach integrates client-side model updates during central server aggregation with Federated Averaging algorithm (FedAvg), dynamically adapting to dataset characteristics. It fosters the development of a robust global model for improved performance across diverse client environments. Utilizing Unet and TransUnet architectures, the models are trained on both native and augmented Endovis2017 dataset samples for optimized segmentation. The performance of both Unet and TransUnet models are validated using metrics such as Dice score, mIoU, and accuracy. TransUnet Model works well and its performance is good at small instrument segmentation compared to Unet Model. The TransUnet model achieved the highest accuracy of 99.43%, with a Dice score of 97.75% and mIoU score of 96.41%.