Antonio Guterre also 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 in Hungary while migrants hoping to reach the Austrian border 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.
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.
