They are among 2,000 people camped at Budapest’s Keleti train station, having bought tickets for onward journeys.
Meanwhile, more than 4,000 migrants arrived in mainland Greece from the island of Lesbos overnight.
The EU is struggling to agree a common policy across member states for dealing with the crisis.
The BBC’s Chris Morris in Brussels says the European Commission, the executive of the EU, is trying to draw up a list of safe countries of origin that failed asylum applicants can be sent back to.
And an EC spokeswoman said today it was preparing proposals for a mechanism to automatically redistribute a proportion of those seeking asylum among EU states.
Italy and Greece have complained that they are overwhelmed by the numbers arriving on their shores.
About 2,000 migrants camped overnight at Keleti station in east Budapest, having been prevented from boarding trains on Tuesday.
They had bought tickets after Hungary appeared to abandon efforts on Monday to register migrants, allowing huge numbers to board trains to Vienna and southern Germany.
Hundreds of migrants again protested on Wednesday, chanting “Freedom, freedom” and waving train tickets.
Journalists at the scene said tensions were high with migrants involved in a stand-off with riot police.
A confrontation also broke out an another railway station in Budapest where a group of migrants occupied a platform after refusing to board a train sending them to a reception centre in the eastern city of Debrecen.
Police quoted by Hungarian TV said the “illegal immigrants” held their children aloft and demanded they be allowed to proceed freely to Germany.
Prime Minister Viktor Orban is due to meet EU chiefs on Thursday to discuss Hungary’s handling of the crisis.
Under an EU rule known as the Dublin Regulation, refugees should seek asylum in the first EU country they enter.
But this has proved hard to uphold, with border countries such as Hungary, Italy and Greece saying they cannot cope with the numbers. All three are members of the borderless Schengen Area.
In another development, border controls between Italy and Austria are set to be reintroduced following a request from Germany, Italian officials said.
The northern province of Bolzano said the German state of Bavaria had asked for “logistical support”.
Bavaria, particularly the city of Munich, has seen record numbers of migrants arriving from the south. Austria is also performing spot checks on its border with Hungary.
The German government has already said it will allow Syrians arriving from other EU states to apply for asylum. But on Tuesday, a spokesman said the Dublin Regulation had not been suspended.
German Chancellor Angela Merkel has called for asylum seekers to be distributed more equally across the EU.
But on Wednesday, UK Prime Minister David Cameron said that taking “more and more” refugees was not the answer.
Greece saw the arrival of 23,000 migrants last week alone, said the EU’s border control agency Frontex – an increase of 50% on the previous week.
Many of those arriving in the country do so on the island of Lesbos, where, according to the Kathimerini newspaper, 17,500 migrants were registered in the last week.
Some 4,200 migrants were brought from Lesbos to the port of Pireaus, near Athens overnight.
Greece’s government says it lacks the resources to look after so many arrivals, but aid groups say the authorities should be doing more.
Greece’s caretaker cabinet is set to convene to discuss the issue later on Wednesday.