Rapid estimates of source parameters are needed for reasons of civil protection in regions where destructive events often occur. This information can prevent further damage and casualties. A relation between the first seconds of a P- wave onset and the local magnitude ML of the earthquake has been developed for the Italy region following results obtained in Japan and Southern California. The proposed dominant period estimate has been used in the present work and it gives reliable results from which to evaluate the size of the earthquake. The data set we evaluated consists of about 20,000 earthquakes that occurred in Italy and were well recorded by the stations of the MedNet Network. The proposed relationship will be one basis for developing and implementing an earthquake early warning system in Italy capable of delivering a rapid alert only a few seconds after the occurrence of a potentially destructive earthquake in the area. Recent extensive improvements of the Italian National Seismic Network, together with this new technique, will make possible the release of a robust magnitude estimate no later than 10 sec after the occurrence of the earthquake. However, no data are available for earthquakes with magnitudes ML >6.0, which poses some reliability limitations for the derived relationship in the case of larger earthquakes.