Mexico's Supreme Court postponed on Wednesday a much-anticipated hearing on a citizen group's bid to legally smoke marijuana, a potential landmark case in a country beset by drug violence, AFP reports.

While dozens of legalization supporters gathered outside the court in the capital's historic center, a judicial official said the justices decided to delay the debate until next week or a later date.

The case was brought by the Mexican Society for Responsible and Tolerant Personal Use, whose Spanish acronym spells "SMART," which is seeking permission to grow and consume its own pot.

Their bid reached the top court after government health regulators refused to grant them a permit.