The cardinal said that the church has never had a problem recommending the use of "all elements from nature that can be used to help improve health."
The federal medical protection agency said the permits apply only to the four plaintiffs who won a favorable ruling from the Supreme Court last month.
Polls show a majority of Mexicans oppose legalization.
The former dean of the National Autonomous University of Mexico disagrees with criminalizing marijuana users.
Óscar Alejandro Rivero Matos was arrested along with two men, one of them a municipal police officer.
The CBP agents discovered the drugs within six boxes identified as aircraft parts in a tractor-trailer driven by a Mexican man.
He said that declaring unconstitutional to prevent people from smoking marijuana would eventually lead to a similar decision for cocaine and heroin.
The new policy follows a wave of changing attitudes toward marijuana that has sparked recent legalization efforts from Mexico to Chile.
Roberto Campa, Human Rights Undersecretary, said that the first phase of the consultation should be completed by March so that Mexico can take a position to the 2016 Special Session of the U.N. on the World Drug Problem.
The chairman of the National Electoral Institute proposed to organize a public consultation on marijuana legalization during the 2018 federal elections.