Federated Learning (FL) and Split Learning (SL) are privacy-preserving Machine-Learning (ML) techniques that enable training ML models over data distributed among clients without requiring direct access to their raw data. Existing FL and SL approaches work on horizontally or vertically partitioned data and cannot handle sequentially partitioned data where segments of multiple-segment sequential data are distributed across clients. In this paper, we propose a novel federated split learning framework, FedSL, to train models on distributed sequential data. The most common ML models to train on sequential data are Recurrent Neural Networks (RNNs). Since the proposed framework is privacy-preserving, segments of multiple-segment sequential data cannot be shared between clients or between clients and server. To circumvent this limitation, we propose a novel SL approach tailored for RNNs. A RNN is split into sub-networks, and each sub-network is trained on one client containing single segments of multiple-segment training sequences. During local training, the sub-networks on different clients communicate with each other to capture latent dependencies between consecutive segments of multiple-segment sequential data on different clients, but without sharing raw data or complete model parameters. After training local sub-networks with local sequential data segments, all clients send their sub-networks to a federated server where sub-networks are aggregated to generate a global model. The experimental results on simulated and real-world datasets demonstrate that the proposed method successfully trains models on distributed sequential data, while preserving privacy, and outperforms previous FL and centralized learning approaches in terms of achieving higher accuracy in fewer communication rounds.