Government agencies worldwide face growing volumes of citizen appeals, with electronic submissions increasing significantly over recent years. Traditional manual processing averages 20 minutes per appeal with only 67% classification accuracy, creating significant bottlenecks in public service delivery. This paper presents AI Appeals Processor, a microservice-based system that integrates natural language processing and deep learning techniques for automated classification and routing of citizen appeals. We evaluate multiple approaches -- including Bag-of-Words with SVM, TF-IDF with SVM, fastText, Word2Vec with LSTM, and BERT -- on a representative dataset of 10,000 real citizen appeals across three primary categories (complaints, applications, and proposals) and seven thematic domains. Our experiments demonstrate that a Word2Vec+LSTM architecture achieves 78% classification accuracy while reducing processing time by 54%, offering an optimal balance between accuracy and computational efficiency compared to transformer-based models.