The UN's High Commissioner for Refugees met with Immigration Minister Chris Alexander on Wednesday as part of a tour that includes Europe and the United States.
Antonio Guterres said today he's hopeful that Alexander will deliver a positive response.
The Canadian government has already agreed to accept 1,300 Syrian refugees who fled the Middle Eastern conflict, but Ottawa remains far from meeting that goal.
Guterres says much more needs to be done to help ease the massive burden on Syria's neighbours, including Lebanon.
He says Syrians now make up more than one quarter of the population in Lebanon, where more than one million people are registered with the UN refugee agency.
Guterres says Lebanon's infrastructures have failed to keep up with the influx of Syrians, leading to overcrowded schools and hospitals.