UNITED NATIONS, United States - At least 13 countries have made inquiries about Canada's private refugee-sponsoring system in the hope of potentially emulating it, the federal immigration minister said Monday during a conference on the historic migration crisis.

John McCallum said the United Kingdom is one of several countries looking at establishing a similar program where private citizens provide funding to bring in refugees and help them get set up in their new home.

McCallum will announce an initiative on private refugee sponsorships Tuesday with the United Nations and billionaire George Soros.

Canada's program was developed under the Pierre Trudeau and Joe Clark governments of the 1970s in response to a migration wave from Vietnam. It has gained new attention amid the wide-ranging effects of Syria's five-year civil war, with other countries now developing similar systems.

"At least 13 countries have expressed an interest in this. That could be one part of the solution for the world at large," McCallum told reporters at the United Nations conference, where Canada announced a 10-per-cent funding increase for international aid.

"So we have had good conversations with a number of countries who may want to follow that practice... I think this is a very useful model that we could export to the rest of the world."

He said the details might vary from one country to the next. Australia began testing a similar model in 2013, and Germany has also followed suit. McCallum said that if countries can enlist their citizens to sponsor refugees and help them get started in a new home, "you're miles ahead."

Under the government plan to resettle 25,000 Syrians by early this year, nearly 9,000 were privately sponsored and another 2,000 were sponsored by a program that blends private and government support.

The program set a cap of private sponsorships allowed per year. It allows people to sponsor a refugee for $12,600, which includes help with income and initial costs like groceries and rent.

McCallum said Canadians would be proud of what he's hearing at this week's United Nations conference: "This is a place where Canada can stand tall. The international community has recognized and strongly supported what we have done."

He noted, however, the numerous challenges ahead. He said refugees to Canada have all been housed - now he says the big hurdles to clear are English- or French-language training, and integration into the job market.

He said the troubles refugees experience should come as no surprise.

"We asked for vulnerable people - we got vulnerable people," he said.

"The other side of that is it takes longer to settle them in."

He suggested Canada might increase its refugee intake next year, after the government sets its annual targets: "Of course I would like to see more. It is a long tradition of Canada to welcome refugees... How many we will welcome - we have to determine that and we'll announce it in November."