"We estimate that in our country the number of those trapped will be from 50,000-70,000 people next month", Migration Minister Yiannis Mouzalas said.
Read more from our special coverage on "MIGRANT CRISIS"
"Today, there are 22,000 refugees and migrants", he added in an interview with Mega Channel tv.
Some 6,500 people were stuck at the Idomeni camp on Greece's northern border with Macedonia as Macedonian border officials let only 300 refugees and migrants pass the day before.
The build-up at the 1,500-people capacity camp began in earnest last week after Macedonia began refusing entry to Afghans and imposed stricter document controls on Syrians and Iraqis.
The bottleneck is expected to get worse after EU members Slovenia and Croatia, as well as Serbia and Macedonia, imposed a limit of 580 migrants entering their borders each day.
Those measures came on the heels of a clampdown by Austria, which lies farther up the migrant trail that extends from the Balkans to Germany and Scandinavia.
Austria introduced a daily cap of 80 asylum-seekers and said it would only admit 3,200 migrants transiting the country.
As a result, the tighter controls have had a big knock-on effect in Greece, where migrants have been arriving in mass from neighbouring Turkey.
Thousands, including many children, are now stranded there as the European Union struggles with the continent's worst migration crisis since the end of World War II.
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