Men and women with furrowed brows sat in pews alongside their children at a Montreal church as volunteers explained what to expect now that they have crossed into Canada from the United States seeking asylum.

They would receive temporary housing stipends and access to medical care. Their kids could go to school. The volunteers handed out small maple-leaf flags.

"I like Canada very much," 26-year-old Marline Dorisma of Haiti said later. "There are lots of opportunities here."

What they did not get were any assurances that they will be allowed to stay. In fact, many will eventually be told to go back home.

The migrants are part of a recent surge of people crossing over from the United States, including some 4,000 in just the last two weeks, that is straining Canada's immigration system to the point where officials turned a domed stadium into a makeshift shelter.

Many said they left fearing deportation due to increased immigration enforcement under President Donald Trump and believing Canada would automatically give them residence, only to experience a rude awakening upon arrival.

It's a widely held misbelief that Transport Minister Marc Garneau sought to dispel during a recent visit to the international border near Quebec, where migrants have been crossing over from northern New York.

"Unless you are being persecuted or fleeing terror or war, you would not qualify as a refugee," Garneau said, "and it's important to combat that misinformation that is out there."

Like in the United States, rules in Canada allow for asylum for people who can demonstrate a well-founded fear of persecution in their homeland based on race, religion, political opinion, nationality or membership in a group like the LBGT community. People can also be accepted if Canada fears they face torture or cruel or unusual punishment if they are deported.

But those deemed to be economic migrants are given orders of deportation through a process that can range from several months to many years.

Last year Canada granted asylum to 63 percent of applicants, for a total of nearly 16,000, according to the Immigration and Refugee Board of Canada. For Haitians it was 52 percent, said Jean-Nicolas Beuze, the representative in Canada for the United Nations High Commissioner for Refugees. That was similar to the acceptance rate for Haitians in the United States, about 48 percent.

Officials, immigration lawyers and other experts say the false belief that Canada will accept all migrants is particularly common among Haitians.

"If these people were aware of the criteria that need to be met in order to be granted refugee status in Canada, and of the likelihood of being turned down and deported from Canada back to Haiti, it's possible many of them would probably have decided not to have left the United States," lawyer Stephane Handfield said.

Authorities say more than 80 percent of the 4,000 who crossed into Quebec recently are from Haiti. The rest include people from India, Mexico, Colombia and Turkey, according to the provincial ministry of immigration.

The Trump administration is considering ending a program that granted temporary residency to about 58,000 people from Haiti following the Caribbean nation's devastating 2010 earthquake. Canada ended a similar program in 2014.

"We're being threatened so we have to leave the country, because we're illegal," said Dorisma. "I was told that Canada isn't a country that deports people."

At Montreal's Olympic Stadium, recent arrivals are sleeping on some 900 cots in a concourse near a rear entrance. Officials say the shelter is operating at 70 to 90 percent capacity at any given time and will be open until next month.

Migrants said they have been encouraged by the reception they have received so far in Canada, where there have been only minor anti-immigration demonstrations.

Inancieu Merilien, one of hundreds of Haitians at the arena, said he and others were "being taken care of very well" and "being here is like a dream come true."

In January, Prime Minister Justin Trudeau tweeted in response to a U.S. ban on travelers from some Muslim-majority nations: "To those fleeing persecution, terror & war, Canadians will welcome you, regardless of your faith. Diversity is our strength."

But the reality is many will be in an uncomfortable limbo while awaiting a decision on their status. Janet Dench, executive director of the Canadian Council of Refugees, said the lingering threat of deportation will make it difficult to build new lives and get good jobs.

"They can't invest in integrating because they don't know what the future holds," Dench said. "So it's an extremely stressful situation."

Also, despite the access to taxpayer-funded medical care and education, the housing assistance doesn't go far. Those subsidies range between about $560 per month for a single adult to $1,900 for a family of four, meaning multiple migrant families often must squeeze in under the same roof.

Joseph Jr. Clormeus, a pastor of Haitian descent who has been helping migrants, said many still prefer Canada to what they faced south of the border.

"Most of them are disoriented, weak, and don't know what the future will bring," Clormeus said. "But they prefer the uncertainty of life in Canada (over) the certainty of being deported from the United States."


Associated Press writer Patrick Lejtenyi reported this story in Montreal and AP writer Rob Gillies reported from Toronto.