Greek officials and the UN have pointed to a growing humanitarian problem along the border between Macedonia and Greece, where up to 70,000 people who fled or otherwise emigrated from the Middle East and beyond will apparently remain stuck.
A NATO plan to crack down on smugglers of people may cut down that number, however.
Four Balkans countries have announced a daily limit on how many people can pass through, and Austria has placed restrictions on entry.
As a result, Greece, which is located at the gateway to Europe, has been flooded with refugees and other migrants who are already numbering over 20,000. These people seek to reach western and northern Europe, but border controls are forcing many into already overcrowded camps according to Al Jazeera, which said only some Iraqis and Syrians have been allowed to cross.
According to Greek officials, the number of refugees trapped in the country may reach 70,000 in the coming weeks.
"We estimate that we will have a number of people trapped in our country which will be between 50,000 and 70,000...in the coming month," Yannis Mouzalas, the Greek immigration minister, told Greek Mega TV on Sunday. About 22,000 migrants and refugees are already in Greece, he said.
NGOs were running out of supplies for the refugees, according to Al Jazeera's reporter, who said there were about 2,000 meals left for at least 7,000 people at a camp at Idomeni.
Last week NATO diplomats said ships already deployed in the Aegean Sea, including Turkish and Greek vessels, would cooperate with the EU border agency to stem the flow of refugees arriving in Europe.
"If the NATO plan is implemented...it could reduce the inflow by about 70%," Greece's Mouzalas said in the TV interview.
Two weeks ago, however, Israeli Defense Minister Moshe Ya'alon said Turkish groups were actually complicit in creating the Muslim migrant invasion of Europe.
He pointed out the role Turkey is playing in "generating" a wave of immigrants from the Middle East going to Europe and emphasized that most are in fact not "refugees," and that they come from numerous Muslim countries, not just war-torn Syria.
Speaking about a recent visit to Greece, he said that while there he learned there is a "well organized system to invade Europe," decrying the "silent Islamic invasion of Europe" that he says is being orchestrated by groups primarily in Turkey.
He said that 800,000 migrants from Morocco were flown in to Turkey in a "deliberate operation," and from there on to Greece.
Ya'alon concluded by calling for a "grand strategy" to confront the problem.