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 have approved tougher border controls and penalties for migrants trying to pass through to their preferred destination, Germany
- Members of the European Commission are in the Greek island of Kos to examine the difficulties caused by the large numbers of refugees and migrants landing there
- The leaders of Poland, the Czech Republic, Slovakia and Hungary will hold an extraordinary summit in Prague
- EU foreign ministers will meet in Brussels
- The UK government - under pressure over its response to the crisis - has agreed to provide settlement for "thousands more" Syrian refugees
- Some 50 migrants are feared to have drowned after their boat sank off the coast of Libya, according to the International Organization for Migration
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.
Migrants or refugees?
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.