According to sources, most of the refugees arriving in Austria gained access through the Nickelsdorf crossing at the Hungarian borders, EFE news reported.
The influx of refugees continued through to Monday, when at least 2,000 people crossed.
Hungary, the main route for refugees arriving in Austria, intercepted at least 23,591 people, while 6,627 were denied access on Sunday, according to the Hungarian police.
Also on Sunday, four trains carrying between 1,500 and 1,800 refugees arrived in the Hungarian town of Hegyeshalom, from where they continued their journey on foot to the Austrian region of Nickelsdorf.
The Hungarian government continues to erect barbed wire fences along its borders with Croatia, as it did with Serbia almost two weeks ago, as part of the measures taken to curb the influx of refugees.
The Hungarian border closure with Serbia resulted in refugees going thorough Croatia, which received some 77,000 people coming through Serbia, who were then led back to the Hungarian borders.