ATHENS, Greece — Greece is fast becoming the “warehouse of human beings” that its government has vowed not to allow.

Hastily setup camps for refugees and other migrants are full. Thousands of people wait through the night, shivering in the cold at the Greek-Macedonian border, in the country’s main port of Piraeus, in squares dotted around Athens, or on dozens of buses parked up and down Greece’s main north-south highway.

On Thursday, hundreds of frustrated men, women and children abandoned their stranded buses or left refugee camps, setting off on a desperate trek dozens of miles long to reach a border they know is quickly shutting down to them.

About 20,000 migrants were in Greece on Thursday, Defense Minister Panos Kammenos said.

Of those, Macedonia allowed just 100 people to cross over from Greece’s Idomeni border area. Another 2,700 people, mostly Syrians and Iraqis, were waiting in a camp at Idomeni at nightfall, while another 1,000 people were stuck at a gas station in Polykastro, 10 miles away.