With tensions growing across a divided EU, the human cost was underlined as the father of Syrian toddler Aylan Kurdi, whose drowning on the crossing to Europe shocked the world, buried his family in their war-torn hometown.
Germany urged an end to "recriminations" as Britain said it would take in thousands more Syrian refugees -- but only direct from camps, not those already in overstretched Hungary, Greece and Italy who are demanding their EU partners do more to help.
In the Hungarian capital, a crowd of migrants put at more than 1,000, including people in wheelchairs and on crutches, set off determined to get to the Austrian border some 175 kilometres (110 miles) away.
"We are very happy that something is happening at last. The next stop is Austria. The children are very tired, Hungary is very bad, we have to go somehow," 23-year-old Osama from Syria told AFP.
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Hungary's right-wing Prime Minister Viktor Orban sparked anger by saying his country did not want more Muslim migrants and warned that Europe would lose its Christian identity, as well as lashing out at Germany for failing to deal with the crisis.
Hungarian lawmakers meanwhile passed tough new anti-immigration measures, including criminalising illegal border crossing and vandalism to a razor-wire fence erected along the border with Serbia.
Some 50,000 migrants arrived in Hungary last month via the western Balkans, with a record 3,300 on Thursday, according to UN figures.