Luca Ceriscioli said quakes and snow had caused landslides and thousands of families were suffering power cuts, with some villages left isolated.
A man was killed and another reported missing in the nearby Abruzzo region.
European Commission President Jean-Claude Juncker vowed EU solidarity with Italy after the tremors.
Marche was one of the regions worst hit by the earthquake of 24 August, with 46 of its 298 victims losing their lives in a single mountain village there, Pescara del Tronto.