Citizenship and Immigration minister Chris Alexander made it clear on Monday, however, that there are no plans to get rid of visas.
He noted that Canada had 10,000 asylum claims from Mexico six years ago.
"Fortunately, under a reform system, that number last year was down to less than 100," he told reporters at Montreal's Pierre Elliott Trudeau International Airport.
Alexander underlined that visas are the norm in Canada's international relations.
The federal minister made the comments after he launched what's called the Can+ program, which will make visa processing quicker for Mexicans who have travelled to Canada or the United States within the last 10 years.
"We are determined to make sure that legitimate travellers from Mexico are coming to Canada in large numbers and growing numbers," Alexander said.
He said Can+ will streamline and expedite visa processing for 50 per cent of Mexicans who travel to Canada and free up agents to work on other cases.
David Goldstein, president and CEO of the Tourism Industry Association, welcomed the news.
The announcement is "an important step forward that will make Canada a more competitive destination, while maintaining the integrity of our immigration system," he said.
The Can+ program builds on a six-month pilot project. It streamlined visa processing, with visas being issued within seven days.
Ninety-five per cent of requests were approved.
Alexander also insisted that Canada's visa service in Mexico is second to none.
"We see the potential of this market because we trust and want to see Mexican students, business people, tourists and family members visiting Canada often," he said. "We are offering service in under seven days to a growing number of people."
Alexander noted that Canada issued Mexicans a total of 69,000 visitor visas and study permits in 2013.
"This year in the first four months, we have 34,000 visitor visas, study permits and worker permits issued — half of last year's numbers in only four months," he boasted.
Under the Can+ program, applicants' passports will be examined for proof of previous travel and their visa applications will then be expedited.
To benefit from the new program, Mexican travellers can apply online or at one of three visa application centres in Mexico.
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