Austria will stop any migrants attempting to rush its border if measures to halt them in Greece and through the Balkans fail, conservative Interior Minister Karl Nehammer said on Sunday.

A massive influx of migrants swelled along the border over the weekend after Turkey's President Recep Tayyip Erdogan threatened to open its frontier to Europe.

Greece has blocked nearly 10,000 migrants trying to enter from the Turkey border over the past 24 hours, a Greek government source said Sunday.

Greek police fired tear gas to repel hundreds of stone-throwing migrants who tried to force their way across the border from Turkey on Sunday, with thousands more behind them after Ankara relaxed curbs on their movement. It was the second straight day of clashes.

The rush echoes Europe's migration crisis in 2015-2016, when Austria served as a corridor into Germany for hundreds of thousands of migrants who traveled through Greece and the Balkans. Austria also took in more than one percent of its population in asylum seekers in the process.

"Hungary has assured us that it will protect its borders as best it can, like Croatia's," Nehammer told broadcaster ORF, referring to two of Austria's neighbors. Migrants coming up through the Balkans would almost certainly have to pass through either of those countries before reaching Austria.

"Should, despite that, people reach us then they must be stopped," he said when asked what Austria would do.

Nehammer's boss, Chancellor Sebastian Kurz, built his career on a hard line on immigration, pledging to prevent a repeat of 2015's influx. He governed in coalition with the far right from 2017 until last year, and is back in power with the Greens as a junior partner.

When Kurz was foreign minister in 2016, Austria coordinated border restrictions in neighboring Balkan countries to stop migrants reaching it from Greece.

Austria is prepared to do the same again if necessary, Kurz and Nehammer have indicated. Kurz is an outspoken critic of Turkish President Tayyip Erdogan's government, a popular stance in his conservative Alpine country.

Turkey said on Thursday it would let migrants cross its borders into Europe, despite a commitment to hold them in its territory under a 2016 deal with the European Union.

Turkey's turnabout came after an airstrike killed 33 Turkish soldiers in Syria, and appeared to be an effort to press for more EU aid in tackling the refugee crisis from Syria's civil war.

"The second safety net, and here the Austrian security services have a lot of previous experience, is close cooperation and also support, whether that be financial, material or in terms of personnel, with countries along the (migrants') escape route," Nehammer said, referring to Balkan countries.