Antonio Guterres, head of the UN refugee agency, said the EU must mobilise "full force" for the crisis, calling it a "defining moment".
EU leaders, split over sharing the refugee burden, are scrambling to agree a response in meetings on Friday.
In Hungary, hundreds of refugees are locked in a stalemate with authorities.
Migrants hoping to reach the Austrian border have refused to disembark from a train surrounded by police in the Hungarian town of Bicske, 40km (25 miles) from Budapest.
Hungarian authorities want to move the migrants to a nearby refugee camp - but the migrants fear registering there will hamper their plans to seek asylum in Germany and other countries.
In the Hungarian capital, Budapest, hundreds of stranded refugees have vowed to "walk to Vienna" because they have not been allowed to board trains onwards.
Hungary has also shut its main border crossing with Serbia after some 300 migrants escaped from a camp in the town of Roszke, prompting a police search operation.
Meanwhile, a Syrian Kurdish child who was drowned while attempting to reach Greece has been buried in his hometown of Kobane on Friday.
The family of Alan Kurdi crossed the border from Turkey to Syria, carrying coffins bearing his body and those of family members who died with him.
Images of the toddler's limp body, washed ashore on a Turkish beach, have been widely circulated, heightening outrage over the migrant crisis.
As the crisis mounts, the EU is facing intense pressure to adopt a cohesive policy towards the migrant flows - the greatest seen globally since World War Two.
Mr Guterres, of the High Commissioner for Refugees (UNHCR), criticised the bloc's "unbalanced and dysfunctional" system that he said had only benefited people smugglers.
He urged the EU to admit up to 200,000 refugees as part of "a mass relocation programme" that had the "mandatory participation" of all member states.
In a statement, Mr Guterres said Europe needed to build "adequate reception capacities", especially in Greece, replacing a "piecemeal" approach with a "common strategy".
In other developments:
Hungarian MPs on Friday are also voting on creating new holding camps for migrants, and on whether the situation constitutes a state of emergency.
Prime Minister Viktor Orban on Thursday described the situation as a "German problem" as Germany was where those arriving in the EU "would like to go".
However, Luxembourg's Foreign Minister Jean Asselborn - who is heading the EU meetings on the crisis - criticised Hungary's conservative leader on German television, saying: "One sometimes has to be ashamed for Viktor Orban."
European Council President Donald Tusk has said at least 100,000 refugees should be distributed across EU states - a sharp increase on a previous European Commission target of 40,000.
German Chancellor Angela Merkel and French President Francois Hollande have said they will present plans for the redistribution of refugees within the EU.
The word migrant is defined in the Oxford English Dictionary as "one who moves, either temporarily or permanently, from one place, area, or country of residence to another".
A refugee is, according to the 1951 Refugee Convention, any person who "owing to a well-founded fear" of persecution is outside their country of nationality and "unable" or "unwilling" to seek the protection of that country. To gain the status, one has to go through the legal process of claiming asylum.
The word migrant has traditionally been considered a neutral term, but some criticise the BBC and other media for using a word they say implies something voluntary, and should not be applied to people fleeing danger.
The euro edged back towards the previous day's five-month high on Tuesday after posting its biggest one-day rise since June, on growing confidence that the market-friendly Emmanuel Macron would beat far-right rival Marine Le Pen to become the next French president.
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Austria said on Sunday it planned to end emergency measures that have allowed thousands of refugees stranded in Hungary into Austria and Germany since Saturday and move step by step "towards normality".
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