Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRU) are a class of Recurrent Neural Networks (RNN) suitable for sequential data processing. Bidirectional LSTM (BLSTM) enables a better understanding of context by learning the future time steps in a bidirectional manner. Moreover, GRU deploys reset and update gates in the hidden layer, which is computationally more efficient than a conventional LSTM. This paper proposes an efficient network model based on deep BLSTM-GRU for ciphertext classification aiming to mark the category to which the ciphertext belongs. The proposed model performance was evaluated using well-known evaluation metrics on two publicly available datasets encrypted with various classical cipher methods and performance was compared against one-dimensional convolutional neural network (1D-CNN) and various other deep learning-based approaches. The experimental results showed that the BLSTM-GRU cell unit network model achieved a high classification accuracy of up to 95.8%. To the best of our knowledge, this is the first time an RNN-based model has been applied for the ciphertext classification.