The incidents are an embarrassing setback for Mr. Calderón, who has hailed the creation of the Federal Police as the future of Mexican policing and one of his biggest accomplishments since taking power in 2006. His government created the force three years ago out of a smaller, existing agency and it was meant to be a trustworthy counterbalance to Mexico's many local and state police forces, which have been mired in corruption.

"Mexico has seen the constant creation and recreation of police forces—it has resulted in a lot of new acronyms but not better policing," said David Shirk, who has studied Mexican policing at the University of San Diego's Trans-Border Institute. "They want to create the new untouchable police entity. So far they haven't..."

The Federal Police have in the past defended their system of lie-detector tests and vetting as helping to keep their force clean.

Mr. García Luna has long said its polygraph tests are accurate and point to other purges since 2010 as evidence of their efficacy.

While vetting new recruits is important, the police also lack a robust internal-affairs department, said Eric L. Olson, who has studied the Mexican Federal Police at the Washington-based think tank Wilson Center.

Mr. Olsen says that as of last year, roughly 95% of the internal investigations under way at the agency involved administrative issues like officers not wearing uniforms or showing up to work. The agency had recently set up a program to catch corrupt cops through sting operations, but had only employed it twice—in both cases to catch police who were asking for minor bribes on roads outside of the industrial hub of Monterrey, Mr. Olson said.