Occasional scuffles broke out and one man was slightly hurt in a stampede. Some disheartened migrants, weary of waiting for transport to a registration center, tried to go back to Serbia but police blocked their way.
"We've been here for two days and the Hungarian government only brings one bus?" said a Syrian man, who gave only his first name, Ali.
"We're asking to go back to Serbia and they are not giving us this right. We're asking to go to Budapest and they are not giving us this right. Why? Why?"
Hungary has made frantic and confused efforts to control the huge tide of migrants transiting the country as they try to reach Germany, leaving many trapped for days outside the border village of Roszke and furious at their treatment by Hungarian authorities. On Tuesday, Prime Minister Viktor Orban announced fresh efforts to complete a wall to keep the refugees out.
Despite the efforts of volunteers offering water and some clothes, there were few amenities at the border. The area was strewn with garbage and more people could be seen walking along railroad tracks in Serbia on their way to Hungary. Many of the travelers had slept outdoors in a field during a cold night. They had hoped to be bused to a registration center, but very few buses appeared.
As they grew more frustrated, some of the migrants tried twice to break free from a police line at a collection point near Roszke but were pushed back.
At Budapest's Keleti train station, migrants were being allowed to board trains bound for Austria and Germany. In many cases, they were segregated from other passengers and told they could only enter certain carriages.
The queue of people waiting to board a train to the West was backing up, with about 300 people waiting for the next train Tuesday afternoon.
Almost all of those passing through Hungary are hoping to reach Germany or other Western European countries with generous welfare benefits and open asylum regulations. Almost none wish to remain in Hungary, which is seen as unwelcoming to asylum-seekers and which does not have the same economic opportunities as much richer Germany.
Around the EU, debate continued over what each country should do. Hungary and other former east bloc countries have resisted accepting refugees, but Germany has thrown its weight behind a scheme to set a quota for each of the 28 EU nations.
Austrian Chancellor Werner Faymann said countries opposed to taking in refugees under an EU-wide quota system should suffer financial penalties.
In Geneva, U.N. official Peter Sutherland said it's "not enough" for countries like the United States and wealthy Persian Gulf states to give money to help Syrian refugees — they must take them in, too.
"Buying your way out of this is not satisfactory," Sutherland said, adding that U.N. agencies are well short of their funding needs for meeting the crisis.
Some 7,000 migrants arrived in Vienna between early Monday and early Tuesday and "almost all of them continued on to Germany," an Austrian police spokesman, Patrick Maierhofer said.
After a stand-off with Hungarian authorities last week that saw thousands of migrants trapped at Keleti and elsewhere, the travelers were greatly relieved when Germany opened its doors to them over the weekend.
Nada Mahmod, a 30-year-old from Syria, delayed her departure from Hungary because she became separated from her 14-year-old son, Mohammad Diar. Her agony ended happily with a reunion, and they boarded a train to the West.
"We lost him in the forest. He went with another group," she told The Associated Press in desperation before the boy was located. "Police in Hungary don't help. Everybody else helps. Not the police."
Poland, the largest of the eastern members, has so far agreed to accept 2,000 refugees and has been widely criticized for lacking solidarity with Germany, which has said it expects to take in 800,000 asylum-seekers this year and is able to absorb half a million per year for a few years.
Poland's defense minister and deputy prime minister, Tomasz Siemoniak, on Tuesday faulted other European nations for lacking a thought-out strategy to handle the crisis and for pushing for EU states to accept quotas of refugees.
He called that a "road to nowhere" which would only encourage more people to come. He also said that Germany should not feel it has the right to teach Poland about solidarity, given that Poland was the birthplace of the Solidarity movement, a mass movement that helped bring down communism in the former Soviet bloc a quarter century ago.
"I think that our position is filled with solidarity and with the vision that we will not solve the problem with such summary, hasty decisions," Siemoniak said.
In Hungary, Orban was quoted in Tuesday's edition of the pro-government Magyar Idok (Hungarian Times) daily newspaper as saying that he was persuaded to deploy more workers to finish the fence along the border after an unannounced inspection of the barrier on Monday.
The 4-meter (13-feet) high fence along the 174-kilometer (109-mile) border with Serbia was supposed to be completed by Aug. 31, but is facing delays. Defense Minister Csaba Hende, who was overseeing the construction being done mostly by soldiers, resigned Monday after Orban's visit because of the slow progress.
Several coils of razor-wire are stretched out along the whole border but it has been regularly breached by migrants, who usually crawl under it. The higher barrier is up only on some sections.
Hungarian police said Tuesday that they have detained more than 169,000 migrants this year, including 2,706 on Monday.
In that same period, the Migration Office has received nearly 158,000 asylum requests.
In Greece, the coast guard said Tuesday its patrol vessels picked up nearly 500 migrants in 11 search and rescue missions over the previous 24 hours in the eastern Aegean Sea.
The people, whose nationalities were not immediately clear, were found in small boats near the islands of Lesbos — which accounts for nearly one in two migrant arrivals in Greece — Samos, Kos and the islet of Agathonissi.
More than 15,000 refugees and migrants are stranded on Lesbos, awaiting screening before they can board a ferry to the Greek mainland — from where they head north through Macedonia, Serbia and Hungary to seek asylum in more prosperous European countries.