Hussen, who is of Somali origin, said the Trump administration had assured Ottawa that Canadians holding dual nationality with those countries would not be affected by the US ban.
He said that people from those seven countries who have a valid Canadian permanent residency card can still enter the United States. However, under the US order, the ban will apply to people from the targeted countries who are passing through Canada.
More than 35,000 Canadians with dual citizenship are also citizens of one of the seven countries, he added.
Hussen did not condemn the US measure but stressed that Canada would continue to pursue an immigration policy based on “compassion” while at the same time protecting the security of its citizens.
“We welcome those fleeing persecution, terror and war,” he said, echoing an open-arm Twitter post by Prime Minister Justin Trudeau on Saturday.
Leaders of a group of Canadian technology companies urged the government to provide “targeted” visas for temporary residence in Canada to those displaced by the Trump order.
“Canadian tech companies understand the power of inclusion and diversity of thought, and that talent and skill know no borders,” the leaders said in a joint open letter.
Hussen, questioned about their proposal, said that Canadian authorities were continuing to monitor developments in the situation, but had not made a decision.
An opposition Canadian party, the New Democratic Party, called Sunday for an emergency debate in parliament on the Trump order. The US ban will have “disastrous implications” for thousands of people, an NDP spokeswoman said.
According to the latest Canadian census, from 2011, one out of five people in the country are foreign-born.
Canada has welcomed more than 39,670 Syrian refugees between November 2015 and early January 2017, according to government figures.