"It is well within the EU's means to give refuge, over a number of years, to one million refugees displaced by the conflicts in Syria and elsewhere," said Zeid Ra'ad Al Hussein.
"This would represent barely 0.2 percent of the EU's population," he told a special debate on migrant rights at the UN Human Rights Council, pointing out that Lebanon has already taken in 26 percent of its population in refugees.
His comments came as surging numbers of migrants and refugees have been risking their lives on rickety boats to reach safety in different parts of the world.
More than 100,000 people have made the perilous journey across the Mediterranean to Europe so far this year, and some 1,800 have drowned trying.
"When people are unable to use regular channels to escape oppression, violence and economic despair, they may attempt, in desperation, to find irregular ones," Zeid said.
Latvian ambassador Raimonds Jansons, speaking on behalf of the EU, insisted the bloc was trying to address the problem.
"The situation that Europe is facing at its southern external borders is unprecedented, not only in terms of the number of migrants and refugees arriving by boat, and the tragic loss of life in the Mediterranean, but also in terms of the response it has triggered" by the EU, he told the council.
According to the International Organization for Migration, nearly 50,000 people have been rescued since the beginning of the year in the waters between Libya's coast and Italy largely thanks to recent increased efforts by Europe to patrol the water routes.
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'Prejudice is combustible'
Zeid commended the EU for its "recent determination to tackle migration in a more comprehensive manner," but insisted a greater shift in approach was needed.
"The resources currently deployed for ineffective border control systems could instead be invested in maximising the benefit of regular migration channels," he insisted.
He said Europeans should recognise the benefits of migrants, and should work harder to counter the "growing bigotry about migrants, which is often suffused with racism and religious hatred and stirred up for political gain."
"Every European knows that racial and religious prejudice is combustible," he said, adding he was "shocked and shamed by the frequent demonisation of migrants."
The top UN expert on the human rights of migrants, Francois Crepeau, also insisted that making it easier to migrate legally was a major part of the puzzle.
"Migrants often have very few options, if any," he said, insisting "sealing borders does not work."
He compared today's lawless situation, where traffickers run rampant, with the Prohibition era in the United States, where "the mafia created by the prohibition policies were only defeated when the sale of alcohol was legalised, regulated and taxed."
"States need to reclaim the mobility market by offering better mobility options than what the smugglers are offering," he said.