Authorities identified the two victims as an elderly woman found dead in her flooded home and a 63-year-old shepherd who was swept away by rising waters.
They said a woman who ignored warnings from firefighters and police not to drive into an area where a bridge spans a river is now missing.
The country’s fire service said it had fielded almost 2,500 calls from trapped residents in central and western Greece, or pleas to remove fallen trees that were blocking roads or had caused property damage.
The service reported rescuing more than 600 people.
Greece’s train operator, Trainose, said service linking southern and northern Greece was suspended.
Water from a river that burst its banks damaged at least two bridges and several buildings, including the local health centre in the Thessaly town of Mouzaki, which has collapsed.
Parts of the stricken area are without electricity.
