Continuous sign language recognition is a weakly supervised task dealing with the identification of continuous sign gestures from video sequences, without any prior knowledge about the temporal boundaries between consecutive signs. Most of the existing methods focus mainly on the extraction of spatio-temporal visual features without exploiting text or contextual information to further improve the recognition accuracy. Moreover, the ability of deep generative models to effectively model data distribution has not been investigated yet in the field of sign language recognition. To this end, a novel approach for context-aware continuous sign language recognition using a generative adversarial network architecture, named as Sign Language Recognition Generative Adversarial Network (SLRGAN), is introduced. The proposed network architecture consists of a generator that recognizes sign language glosses by extracting spatial and temporal features from video sequences, as well as a discriminator that evaluates the quality of the generator's predictions by modeling text information at the sentence and gloss levels. The paper also investigates the importance of contextual information on sign language conversations for both Deaf-to-Deaf and Deaf-to-hearing communication. Contextual information, in the form of hidden states extracted from the previous sentence, is fed into the bidirectional long short-term memory module of the generator to improve the recognition accuracy of the network. At the final stage, sign language translation is performed by a transformer network, which converts sign language glosses to natural language text. Our proposed method achieved word error rates of 23.4%, 2.1% and 2.26% on the RWTH-Phoenix-Weather-2014 and the Chinese Sign Language (CSL) and Greek Sign Language (GSL) Signer Independent (SI) datasets, respectively.