UNHCR chief Filippo Grandi also urged humanitarian access throughout Syria, describing images of starving children in the war-torn country as "unacceptable".
Grandi renewed a longstanding UN call for more aid for the countries neighbouring Syria that are hosting most of the more than four million people who have fled the conflict since it began in March 2011.
But he also urged wealthy nations to provide alternatives to the illegal smuggling routes that waves of refugees have used to flee in the past year.
"It's cheaper for everybody, more orderly for those countries and it's so much better and safe for the refugees themselves," he added.
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Since last year Europe has been rocked by its biggest migration crisis since World War II, with hundreds of thousands of people fleeing war and poverty arriving on its shores.
Many of those coming are fleeing Syria's conflict, which has killed more than 260,000 people.
"We need to multiply legal opportunities for people to travel safely," Grandi said.
The Italian diplomat, who took the helm of the UNCHR on January 1, also said he had urged Syria's government to provide greater humanitarian access, during a visit to Damascus this week.
"I told them that it was unacceptable that images of starving children in besieged areas would be all over the media, that this was a shame on Syria," he said.
Grandi said the Syrian government had told him to appeal to "other parties" to ensure access, and he urged "all those who have influence" to push for greater aid access as well as a peace process.