Canada has begun revoking citizenship from 3,100 people that the government said obtained it fraudulently, the country's immigration minister said Monday.

Immigration Minister Jason Kenney said that in most of the fraud cases, applicants paid a representative to prove they were living in Canada to establish residency when they were, in fact, living abroad.

Permanent residents must reside in Canada for three out of four consecutive years before applying for Canadian citizenship. To retain their status as permanent residents, they must live in Canada for two out of five years, with rare exceptions.

Criminal investigations by the Royal Canadian Mounted Police and the Canadian Border Services Agency have found that a family of five could pay over $25,000 over four or more years to create the illusion of Canadian residence.

The government said it is also investigating thousands of others who may have lied to obtain or maintain permanent residency. Kenney said anyone caught committing fraud will be stripped of citizenship and residence status.

"Canadian citizenship is not for sale," Kenney said during a news conference Monday. "We will not stand idly by and allow people to lie and cheat their way into Canadian citizenship."

Kenney has said that Canada's per-capita immigration rate remains one of the highest in the world, with the country welcoming 248,660 permanent residents in 2011. An average of about 250,000 immigrants has been admitted to Canada annually since 2006, which the immigration department calls the highest sustained level of immigration in Canadian history.

The minister said a crack-down on immigration fraud started three years ago, with nearly 11,000 individuals potentially implicated in lying to apply for citizenship or maintain permanent resident status.

He said federal agencies have so far removed or denied admittance to more than 600 former permanent residents linked to the investigations.

Kenney also said he is planning to introduce amendments to the Citizenship Act that would require immigration consultants to be members of a regulatory body, which he said may help crack down on crooked consultants.