Austria's railway company has suspended train services to and from Hungary because the volume of refugees and migrants entering the country is causing overcrowding.
It said the cross-border suspension would last for at least a day.
Record numbers of asylum seekers have streamed through the Balkans into Hungary, as Europe remains divided over how to cope with the crisis.
Germany has warned that a European Union plan to distribute 160,000 new arrivals among member states was a mere "drop in the ocean".
Hungarian police said 3,321 people had entered in just 24 hours, hurrying to cross before harsh new anti-migrant laws take effect, a fence is completed, and the weather worsens.
Hungary said it expected to finish building the 4m high fence in the next few weeks.
The United Nation's refugee agency earlier warned that at least 42,000 people were expected to enter Hungary by next week.
Hungary is preparing to declare a state of crisis due to the influx. The declaration, to be discussed by the government next week, would make crossing the border fence a criminal offence.
That could result in refugees and migrants being expelled from Hungary.
Hungary's parliament was also expected to discuss sending the army to the border to help with patrols.
More than 160,000 people have entered the country from the south this year. Many are trying to travel through Hungary to Germany, Austria and Sweden - wealthier European Union nations with more liberal asylum laws.
Meanwhile, Serbian media report that a record 5000 asylum-seekers travelling north have arrived at the Serbo-Hungarian border in the past 24 hours.
Most of the thousands of refugees streaming into Europe have fled conflict in Syria and Iraq, as well as North African countries.
Other countries increase intake
Meanwhile Ireland, which has a population comparable to New Zealand's, has announced it will accept a total of 4000 refugees from the crisis in Europe.
The Irish Justice Minister said the republic had agreed to resettle up to 2,900 more refugees than the 600 it had earlier offered to take.
The country is already in the process of resettling 520 people.
Ireland is a member of the European Union but has not signed up to the EU's plan to share refugees across the bloc.
On Wednesday, the European Commission President, Jean-Claude Juncker, announced plans to distribute 120,000 refugees from Greece, Italy and Hungary among member states via binding quotas.
The United States president, Barack Obama, has told his administration to prepare to take in at least ten-thousand Syrian refugees next year, to help address the growing refugee crisis.
A White House spokesperson said the number reflected a significant scaling up of the country's commitment to accept refugees from the war-torn country.
US-led coalition bombs Syria, Iraq
A coalition led by the United States bombarded Islamic State militants with 10 air strikes in Syria and 18 in Iraq on Wednesday, according to a statement released on Thursday.
The Combined Joint Task Force said the air strikes in Iraq - near Tuz, Sinjar, Mosul, Ramadi and other locations - hit tactical units and fighting positions and destroyed vehicles, buildings and two light machine guns belonging to the militant group IS.
In Syria, the area around Hasaka bore the brunt, with three air strikes hitting IS tactical units and destroying three fighting positions, two motorcycles and a structure, it said. An air strike near Al Hawl and another near Palmyra had inconclusive results.
- BBC, ABC, Reuters