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

Hastily set up 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.

By late Friday, not a single migrant had crossed into Macedonia that day, while 4,900 people waited nearby in heavy rain, according to Greek police.

Thousands more were heading north — about 40 busloads of people were waiting along Greece’s main highway, while refugee camps in the north and near Athens were full.

Greece is mired in a full-blown diplomatic dispute with some EU countries over their border slowdowns and closures. Those border moves have left Greece and the migrants caught between an increasingly fractious Europe, where several countries are reluctant to accept more asylum-seekers, and Turkey, which has appeared unwilling or unable to stanch the torrent of people leaving in barely seaworthy smuggling boats for Greek islands.

Adding to the pressure is Greece’s financial predicament. The country has been racked by a financial crisis since 2010 and still depends on an international bailout for which it must pass yet more painful reforms. Those have led to widespread protests, including blockades on the country’s highways by farmers who are furious at pension changes.

The vast majority of those reaching Greece, Europe’s main gateway for migrants, have been Syrians, Afghans, and Iraqis fleeing war at home.

“My only hope is to live in a safe place. That’s enough for me, actually,’’ said Minhaj Ud Din Wahaj, 17, from Afghanistan’s Wardak province. ‘‘We have been in war since 40 years, so I have been raised in war.’’

In Athens, hundreds of migrants mill around central Victoria Square, uncertain of where to go next. On Thursday, two men tried to hang themselves from a tree in the square but were rescued by bystanders. Police said the men were trying to draw attention to their predicament.

In the north, nearly 400 people scrambled out of a former military base set up as a refugee camp in Diavata, near the city of Thessaloniki, and began walking the 43 miles to Idomeni on the Macedonian border. Dozens more set off on foot from buses stuck on the highway, where farmers’ blockades were hindering traffic.

Still more people flowed into the country, with dinghies full of migrants arriving on Greece’s islands and hundreds more people piling on ferries heading to the main port of Piraeus.

“We are escaping from war,’’ said Rana, an English teacher from Syria arriving in Piraeus. She would not give her last name to protect those she left behind. “Our house is destroyed, and salaries in some places stopped. . . . I think all the people . . . seek the shelter and education for their kids.’’

But Europe appears increasingly unwilling to provide those basics. On the weekend of Feb. 20-21, Macedonia stopped allowing Afghans through. Other countries further up the line appeared to do the same. On Thursday, even Syrians and Iraqis were being allowed to cross over from Greece only at a trickle. Nadica V’ckova, a spokeswoman for Macedonia’s crisis management department, said Macedonia was restricting the entry of refugees to match the number leaving the country.