She added that the new proposals would bring Canada in line with the regional approach to the issue of immigration.
The move reverses earlier suggestions that all applicants who tested positive would be turned away.
Immigration Minister Elinor Caplan told parliament that the status of would-be immigrants who test positive in new mandatory HIV checks would be decided on a case by case basis.
Opponents of the bill say it will cost Canada almost $30m a year in additional medical costs to care for immigrants with Aids.
Canada currently admits 225,000 immigrants a year.
Relief
Seeking to allay fears of discrimination against people applying for immigration to Canada, Ms Caplan insisted that refugees and relatives of people already in Canada would still be admitted regardless of the result of medical tests.
And other instances would be decided by the provincial governments on a case by case basis, she said.
She added that the new proposals would bring Canada in line with the regional approach to the issue of immigration.
"Once someone is tested, then they have the opportunity for counselling and treatment, and that's extremely important. I think the testing policy is a thoughtful one, which is also consistent with the United States and Australia and other countries that are receiving immigrants," the minister said.
At present, only those prospective immigrants whose doctors suspect they might be suffering from HIV are tested. Health officials say around 50 to 70 potential immigrants a year are rejected after testing positive.
Costly
Inky Mark, opposition MP with the right-wing Canadian Alliance, said the new proposals would overburden the country's health care system.
He said about 200 HIV-positive immigrants allowed into Canada last year had cost the taxpayers an extra $26m.
But Ralf Juergens, head of the Canadian HIV/Aids Legal Network, said he still feared the authorities would deny entry to HIV-infected immigrants, which he described as "unjust".
"We are worried about the fact that the vast majority of people would still be excluded based on an assumption that they would create excessive demand on health and social services," he told a news conference.
The BBC's Ian Gunn says the government argues that its new policy balances public health concerns, the rights of immigrants and still protects a domestic health system that is already under financial strain.