The Greek government announced on Sunday that it would set up a health centre for refugees massing on the border with the former Yugoslav republic of Macedonia.
The centre in the border town of Idomeni should be operational by Wednesday, the government said.
Media and humanitarian organizations estimate that the number of migrants at the Greek-Macedonian border crossing had swelled to 14,000 by Sunday morning.
Many of them are living in makeshift tents, with children suffering colds and breathing complaints in the cold and damp conditions.
Governor Apostolos Tzitzikostas has called on the government to declare a state of emergency in the region.
Macedonia has closed its borders to the wave of refugees wanting to pass through its territory to reach richer nations in western and northern Europe, straining bilateral ties with Greece.
The Greek Foreign Ministry has threatened Macedonia with unspecified serious consequences if it does not let the refugees pass through.