Phishing is one of the most dangerous attacks targeting individuals, organizations, and nations. Although many traditional methods for email phishing detection exist, there is a need to improve accuracy and reduce false-positive rates. Our work investigates one-dimensional CNN-based models (1D-CNNPD) to detect phishing emails in order to address these challenges. Additionally, further improvement is achieved with the augmentation of the base 1D-CNNPD model with recurrent layers, namely, LSTM, Bi-LSTM, GRU, and Bi-GRU, and experimented with the four resulting models. Two benchmark datasets were used to evaluate the performance of our models: Phishing Corpus and Spam Assassin. Our results indicate that, in general, the augmentations improve the performance of the 1D-CNNPD base model. Specifically, the 1D-CNNPD with Bi-GRU yields the best results. Overall, the performance of our models is comparable to the state of the art of CNN-based phishing email detection. The Advanced 1D-CNNPD with Leaky ReLU and Bi-GRU achieved 100% precision, 99.68% accuracy, an F1 score of 99.66%, and a recall of 99.32%. We observe that increasing model depth typically leads to an initial performance improvement, succeeded by a decline. In conclusion, this study highlights the effectiveness of augmented 1D-CNNPD models in detecting phishing emails with improved accuracy. The reported performance measure values indicate the potential of these models in advancing the implementation of cybersecurity solutions to combat email phishing attacks.