Around 1,000 people waved tickets, clapping, booing and hissing, and shouting "Germany! Germany!" outside the station.
Later they sat down, staring at a police blockade erected at the entrance.
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The decision to bar the migrants from westbound trains was a reversal from the previous day, when Hungary and Austria let trainloads of undocumented migrants leave for Germany, a violation of EU rules they now have little power to enforce. The arrival of hundreds of thousands of migrants has confounded Europe, which has eliminated border controls for travel between 26 countries of its Schengen area but requires those seeking asylum to remain in the country where they first arrive until their applications are processed.
The vast majority of refugees fleeing violence and other migrants escaping poverty first arrive on Europe's southern and eastern edges but are determined to press on and seek asylum in richer and more generous countries further north and west. Hungary is on a major overland transit route from West Asia and Africa through Greece and the Balkans to Germany. More than 140,000 people have crossed into Hungary from Serbia this year alone.
European leaders want the EU to do more to organise the unprecedented influx, help separate those deserving asylum from those who can be safely sent home and share the burden of accepting them across the 28-nation bloc.
German Chancellor Angela Merkel said refugees with valid asylum claims should be distributed among EU countries according to their capacity to host them.
"For those refugees who are being persecuted or have fled war, there should be a fair distribution in Europe based on the economic strength, productivity and size of each country," she told a joint news conference in Berlin with Spanish Prime Minister Mariano Rajoy.
For now, however, there is no mechanism in place to distribute refugees or to enforce the so-called "Dublin rules", which require asylum seekers to apply in the first EU country where they arrive.
Berlin said the Dublin rules must still be enforced.
"Whoever comes to Hungary must get registered there and go through the asylum procedure there," a German Interior Ministry spokesman said.
German Labour Minister Andrea Nahles said the influx of refugees and migrants would mean an additional 240,000-460,000 people would be entitled to German social benefits next year, costing the government Euro 3.3 billion ($3.7 billion).
Where should we go?
For Hungary, the main entry point for those arriving in the EU over land across the Balkans, the crisis has prompted the government to reinforce the border with a razor wire fence and deploy thousands of extra police.
Faced with the enormous pressure of thousands upon thousands of migrants arriving in Budapest, Hungary let them board westbound trains on Monday before unexpectedly shuttering the train station again on Tuesday morning.
Government spokesman Zoltan Kovacs, when asked why the railway terminus was closed, said Hungary was trying to enforce EU law, which requires anyone who wishes to travel within Europe to hold a valid passport and a Schengen visa.
Marah, a 20 year-old woman from Aleppo, Syria, said her family had bought six tickets for a RailJet train that was scheduled to leave for Vienna at 9 am on Tuesday.
"They should find a solution," she told Reuters. "We are thousands here, where should we go?"
The crisis has polarised Europe, which, on the one hand, is committed to the principle of providing refuge for those in danger, but on the other hand has a growing sector of public opinion that believes too much immigration drives down wages and dilutes national cultures.
Thousands of migrants have drowned this year attempting to reach Europe across the Mediterranean Sea in rickety vessels, while the perils of the overland part of the journey were hammered home when 71 people were found dead in an abandoned truck in Austria last week.
Political parties that oppose immigration have gained ground across Europe, not least in Hungary itself, where Prime Minister Viktor Orban's ruling centre-right Fidesz party has struck a combative tone. Antal Rogan, the party's parliament caucus leader, said on Tuesday "the very existence of Christian Europe" was under threat.
"Would we like our grandchildren to grow up in a United European Caliphate? My answer to that is no," Rogan told the pro-government daily Magyar Idok.
Orban's chief of staff, Janos Lazar, told a parliamentary committee that immigration must be controlled tightly.
"I do not think Hungary would need a single immigrant from Africa or the Middle East," Lazar said. "Europe must use its own human resources fundamentally and if it wants an immigration policy it must be regulated and controlled." "In the past decade ... a leftist view has dominated the European Commission and the European Parliament, that the way to develop Europe was through allowing everyone in and accepting everyone without checks, rules and controls."
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