Almost all of those arrivals were at the town of Nickelsdorf, which has generally been the main crossing point for migrants coming from Hungary. Buses and trains took many on to emergency accommodation elsewhere, and others took taxis, a Reuters witness said.
Another police spokesman said Vienna-bound lanes on the A4 motorway, which goes through the border near Nickelsdorf, were closed for security reasons, without elaborating. The police have previously closed lanes of that motorway because of migrants setting off for Vienna on foot.
A spokesman for motorists' group OeAMTC later said the lanes had reopened, but there were traffic jams.
In Styria, a southeastern province that borders Slovenia, 500 migrants entered the country on Sunday, a spokesman for the police in that province said.
Read MoreMigrants stranded as EU border crackdown continues
Meanwhile, 13 migrants died on Sunday in Turkish waters when a boat carrying 46 people en route to Greece collided with a dry cargo vessel and capsized, a Turkish coast guard source said.
Six of those killed were children and 20 others were rescued, the source said. Seven of those rescued were receiving treatment.
The boat had left the Turkish coast near Canakkale province.
The search continues to find 13 missing people.