More than 100 migrants an hour have arrived in Germany amid a record influx travelling on packed trains to the southern city of Munich, police say.
An average of 109 illegal entries an hour were registered between midnight and 6:00am on Wednesday (local time) nationwide, federal police said.
The national total for Tuesday was 3709, more than twice the daily average of recent weeks, with most arriving in Munich by rail from Hungary via Austria.
Europe's most populous nation and biggest economy, Germany has become the top EU destination for refugees and migrants fleeing conflict and misery.
In Budapest, around 100 to 150 migrants staged a demonstration outside the main international train station as police blocked about 2000 people from boarding trains to Austria and Germany, an AFP reporter said.
Around 600 men, women and children, mostly from Syria, Iraq and Afghanistan, sat or stood outside the Keleti station while about 1200 were downstairs in a so-called "transit zone".
Around 100 migrants arriving from a registration centre near the border with Serbia sat on the platform at a suburban train station, refusing to board a train to the Debrecen refugee camp.
Police said in a statement that the group "demanded to be allowed to travel on to Germany.... Police have taken the necessary security steps to ensure that train traffic is undisturbed."
Hungary, which saw 50,000 migrants enter the country in August alone, this week allowed thousands to board trains to Austria and Germany, but in a U-turn on Tuesday, police suddenly blocked access to the station for anyone without an EU visa.
Only around 150 migrants arrived in Vienna by train from Budapest on Tuesday afternoon, police said. On Monday, a record 3650 arrived.
The Hungarian government of right-wing Prime Minister Viktor Orban, which has built a razor-wire barrier along its 175-kilometre border with Serbia, said that it was applying EU rules.
"Normal people, abnormal people, educated, uneducated, doctors, engineers, any people, we're staying here. Until we go by train to Germany," said Mohammad, a Syrian protesting at the station.
"And this is what we will be doing (protesting) for the next day, for the next month, for the next year and for our whole life. We need our rights.... It's not our dream to stay here and to sleep in the streets."
Hungary's razor-wire barrier is proving ineffective in keeping out the tens of thousands of people trekking up from Greece through the western Balkans, with Hungarian authorities saying that 2284 crossed on Tuesday, including 353 children.
"If Europe is letting us in, why don't they give us visas? Why do we have to make this clandestine journey?" Bilal, a Syrian from the divided city of Aleppo, said on Tuesday near Serbia's border with Hungary.
"We fear that one day everything will change, that even Germany will close the border when it has had enough, so we must make our journey extremely fast," he said.
Meanwhile Greek ministers were set to meet on Wednesday morning on the crisis, which is likely to be at the centre of talks scheduled on Thursday in Athens between Greek officials, the European Commission's vice-president Frans Timmermans, and Dimitris Avramopoulos, the EU's Migration and Home Affairs Commissioner.
About 4300 more people arrived in Athens overnight, most of them Syrian refugees.
Two ships carrying the latest arrivals docked at Athens' Piraeus port after sailing from Lesbos, one of several Greek islands struggling to cope with the huge waves of people crossing the Mediterranean from Turkey in flimsy boats.
About 1800 people arrived on the Greek mainland on Tuesday evening, with another 2500 landing at dawn, port police said, adding that they had been taken to a nearby train station.
The ships were chartered by the Greek government to help relieve pressure on Lesbos, whose authorities and infrastructure are ill-equipped to deal with the huge influx of people.