The analysis and characterization of atrial tachyarrhythmias requires, in a previous step, the extraction of the atrial activity (AA) free from ventricular activity and other artefacts. This contribution adopts the blind source separation (BSS) approach to AA estimation from multilead electrocardiograms (ECGs). Previously proposed BSS methods for AA extraction--e.g., independent component analysis (ICA)--exploit only the spatial diversity introduced by the multiple spatially-separated electrodes. However, AA typically shows certain degree of temporal correlation, with a narrowband spectrum featuring a main frequency peak around 3.5-9 Hz. Taking advantage of this observation, we put forward a novel two-step BSS-based technique which exploits both spatial and temporal information contained in the recorded ECG signals. The spatiotemporal BSS algorithm is validated on simulated and real ECGs from a significant number of atrial fibrillation (AF) and atrial flutter (AFL) episodes, and proves consistently superior to a spatial-only ICA method. In simulated ECGs, a new methodology for the synthetic generation of realistic AF episodes is proposed, which includes a judicious comparison between the known AA content and the estimated AA sources. Using this methodology, the ICA technique obtains correlation indexes of 0.751, whereas the proposed approach obtains a correlation of 0.830 and an error in the estimated signal reduced by a factor of 40%. In real ECG recordings, we propose to measure performance by the spectral concentration (SC) around the main frequency peak. The spatiotemporal algorithm outperforms the ICA method, obtaining a SC of 58.8% and 44.7%, respectively.