Fetal heart rate (FHR) monitoring is an important part of antenatal care, providing important indicators of fetal health and diagnosis of fetal disease. Non-invasive fetal electrocardiograms (NI-FECG) for FHR monitoring has received much attention due to its suitability for continuous monitoring, unlike other currently used technologies. However, NI-FECG utilises an abdominally recorded ECG (AECG), which is a mix of maternal and fetal ECG along with other noise signals. Due to the low SNR of the FECG signal, extraction of the FECG to determine FHR is a challenging task. In recent years, various deep learning based methods have shown promising results in predicting fetal R-peak locations used to find the FHR. Most of these methods begin by predicting and cancelling the maternal ECG (MECG) signal prior to a second fetal R-peak detection process. This work proposes an R-peak detection method based on the U-Net architecture for direct detection of fetal R-peaks from the AECG without the need for prior cancelling of the MECG. The proposed method includes a deep learning model based on a shallow U-Net structure, combined with Bidirectional Long-Short Term Memory (Bi-LSTM) and residual paths. Performance of the proposed detection method is evaluated on AECG recordings from set-A of the PCDB PhysioNet database. The proposed method was compared with five other approaches which perform direct fetal R-peak detection using machine or deep learning. Numerical results demonstrate that the proposed UNet-BiLSTM model has reliable performance for fetal R-peak detection from AECG signals, reaching 93.73%, 91.10% and 92.35% in average PPV, Recall and F1-scores, respectively, outperforming the other methods evaluated.