Germany -- itself under fire from eastern neighbours over its willingness to take in refugees -- warned that an EU 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, an imposing new fence is completed, and the weather worsens.
Across the border in Serbia, state television reported that a record 5,000 people had arrived at the frontier.
The UN's refugee agency on Tuesday warned that at least 42,000 migrants were expected to enter Hungary by next week.
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Many have endured treacherous sea journeys across the Mediterranean -- most fleeing war and poverty in Syria, Afghanistan or Pakistan and hoping to reach Germany.
Once inside Hungary, overstretched police have struggled to control and register the new arrivals who mostly board trains and buses bound for the border with Austria.
Emergency measures allowing migrants to enter Austria after the arrival of 15,000 last weekend remained in place. Overnight, 3,700 more crossed the border, Austrian police said.
But Austria's train operator on Thursday suspended services with Hungary because of "massive overcrowding", calling on bus companies and volunteers to stop bringing migrants to stations.
Denmark's trains, which had been suspended Wednesday, were due to start running again, and police said they were letting refugees travel freely towards Sweden, another preferred destination.
In an effort to control the crisis, European Commission chief Jean-Claude Juncker yesterday unveiled a new plan to for the bloc to share out 160,000 refugees to ease the burden on frontline states.
But Germany, which said it has already welcomed 450,000 migrants and refugees this year, wants the 28-nation bloc to go further.
Europe's biggest economy wants compulsory long-term EU quotas with no limits on numbers, with Deputy Chancellor Sigmar Gabriel today likening Juncker's proposals to "a drop in the ocean".