Due to the very low power of satellite signals when reaching the earth's surface, global navigation satellite system receivers are vulnerable to various types of radio frequency interference, and, therefore, countermeasures are necessary. In the case of a narrowband interference (NBI), the adaptive notch filtering technique has been extensively investigated. However, the research on the topic has focused on the adaptation of the notch frequency, but not of the notch width. We present a fully adaptive solution to counter NBI. The technique is capable of detecting and characterizing any number of narrow interfered bands, and then optimizing the mitigation process based on such characterization, namely the estimates of both interference frequency and width. Its full adaptiveness makes it suitable to cope with the unpredictable and diverse nature of unintentional interfering events. In addition to a thorough performance evaluation of the proposed method, which shows its benefits in terms of signal quality improvement, an analysis of the impact of different NBI profiles on GPS L1 C/A and Galileo E1 is also conducted.