Attorneys Juan Pablo Badillo Soto and Jose Luis Gonzalez Meza held a press conference on Friday to announce that they submitted the motion on Thursday, EFE news reported.
The case will likely be decided by Mexico’s Supreme Court, Gonzalez Meza said.
“It’s going to take a long time to bring Chapo to the US,” he said, suggesting that the extradition may never take place.
By handing over Guzman to the US, the Mexican government “would violate the entire rule of law and, specifically, the constitution,” Badillo said.
He accused President Enrique Pena Nieto, Government Secretary Miguel Angel Osorio and Foreign Secretary Claudia Ruiz Massieu of “trampling” on Mexico’s charter and said that Guzman’s family would never see him again if he were extradited.
Earlier this week, another member of Chapo’s defence team said the Sinaloa cartel boss would not oppose extradition if he reached an agreement with US authorities.
“Joaquin is not against facing justice in the US and an agreement would be the way to resolve the problem. If it happens, we’ll forgo the appeals process,” defence team member Jose Refugio Rodriguez said.
Rodriguez said he and Guzman’s U. lawyer, William Stuttgart, would try to negotiate a deal with US prosecutors.
Stuttgart plans to meet soon with Guzman at the prison where the drug lord is being held in Ciudad Juarez, located across the border from El Paso, Texas, Rodriguez said.
Guzman was transferred to the prison in the border city on May 7 from the Altiplano maximum-security prison in central Mexico.
The Mexican government had opposed extradition but reversed course after Guzman escaped from Altiplano on July 11, 2015, through a mile-long tunnel dug to his cell.
He had earlier broken out of a prison in the western state of Jalisco in 2001 and spent more than 13 years on the run before being recaptured on February 22, 2014, in the Pacific resort city of Mazatlan.
Guzman’s organisation rose to become one of the main sources of illicit drugs entering the US.
The Mexican kingpin’s wealth led to his name regularly appearing on Forbes magazine’s list of global billionaires.