Abdominal electrocardiogram (AECG) gives a safe and non-invasive way to monitor fetal well-being during pregnancy using surface electrodes. However, it is challenging to extract weak fetal ECG (fECG) from the AECG recordings with larger maternal ECG (mECG) and external noises. In this study, we introduce a novel progressive periodic source peel-off (PPSP) method for extracting periodic ECG sources from multi-channel AECG recordings, including three main modules: 1) A periodic constrained FastICA (PCFICA) module with ECG physiology-informed constraints for extracting precise ECG spike trains, 2) A singular value decomposition module for estimating ECG waveforms, and 3) A peel-off strategy that facilitates to discern weak fECG source by eliminating previously separated sources or noises. The performance of the PPSP method was examined on two public databases, synthetic data and our clinical data. For extracting fECG spike trains, our PPSP method achieved an F1-scores of 99.59% on public data, 99.50% on synthetic data at the highest noise level. It further yielded the lowest RMSE of fetal heart rate of 6.20% on clinical data. It significantly outperformed other state-of-the-art methods on any set of data (p < 0.05). This study demonstrated effectiveness of the PPSP method for extracting and separating mECG and weak fECG signals, with high precision especially at high noise levels. Our study promotes noninvasive measurement and intelligent monitoring of both fetal and maternal heart activities towards advanced healthcare in perinatal medicine.