Speaking during a visit to a refugee camp in Jordan, Filippo Grandi said the crisis "cannot only concern the countries neighbouring Syria".
Jordan is hosting 633,000 of the 4.39 million Syrians registered as refugees with the UN.
Many Syrian refugees are also sheltering in Turkey and Lebanon.
Hundreds of thousands of others have sought refuge in the European Union in recent years.
"I think we need to be much more ambitious'' about resettling refugees, Mr Grandi, an Italian diplomat, said at the Zaatari refugee camp.
"What is needed is a better sharing of responsibilities," he added.
His comments came as the UN refugee agency (UNHCR) said the number of Syrians stranded on the Jordanian border had risen sharply to about 17,000 people.
Mr Grandi also said the UNHCR would organise a conference in Geneva in March to find host nations for Syrian refugees, after a fund-raising event in London planned for next month.
The Syrian conflict erupted in 2011 with mass protests against President Bashar al-Assad.
More than 230,000 people are estimated to have been killed since then.
The world should find fairer ways of resettling Syrian refugees fleeing the war in their country, the new UN refugee agency chief has said.