So far, Mexico has reported 152 deaths linked to the outbreak. The US has confirmed 64 cases, Canada 13, New Zealand 11, Scotland two and Spain one.
Of the seven new cases in Canada Tuesday, four were reported around Toronto in Ontario province, two in Alberta province, and one in British Columbia.
Authorities said all the new cases were linked to the Mexican outbreak as either the affected people or someone from their families had just returned from that country.
Since the swine flu virus has an incubation period of two to seven days, they feared that many more cases will come to light in the coming days.
Canada's chief medical officer David Butler-Jones appealed to people to contact health authorities immediately if they show symptoms of the virus.
Refusing to say whether the virus will be contained, he said, "Nature is always inventive, and it can go in either direction.''
Referring to the 1918 Spanish flu pandemic that killed 50 million people worldwide, the top health official said: "You can have severe presentation in Mexico... or it could be, as in 1918, where the first round was relatively mild and the next round was much more severe.''
Canadian Health Minister Leona Aglukkaq said though the new cases were mild, they further raised the possibility of the swine flu spreading to become a pandemic.
"While we are not in a pandemic, it simply means that the risk of one has increased,'' the health minister said.
Outlining the government's six-point emergency plan to deal with the swine flu threat, she said the measures included surveillance, closer cooperation with other governments and global agencies, vaccine development, stockpiles of anti-viral medication, quick medical services and communications.
She said travelers from Mexico were being subjected to "enhanced screening" at the country's airports.
Toronto, where 44 people were killed by the severe acute respiratory syndrome (SARS) in 2003, reported its first four cases of the swine flu Tuesday.
Though the cases were reportedly mild as the affected people were recovering, Toronto's chief medical officer David Williams warned that there could be many more confirmed cases of the virus as thousands of people from the city visit Mexico each month.
"Personally, I know we're going to see a lot more cases. It's only a matter of time because of the amount of flow of public that go back and forth to Mexico,'' he said.