The Mexican government says that drug lord Joaquin "El Chapo" Guzman is pursuing a campaign to try to loosen the security measures at the maximum-security prison where he has already escaped once.
National security commissioner Renato Sales told reporters the media strategy was suggested by recent statements made by a purported daughter of Guzman to the British newspaper The Guardian charging the government had betrayed the purported cartel leader.
Sales said those allegations lacked proof, insisting the government made no deals with Guzman.
"Not treaties, nor alliances, nor pacts with (organized) crime," he said. "We will not give in to speculation whose only objective is to divert attention, make this subject a victim to loosen his security."
One of Guzman's lawyers, Jose Refugio Rodriguez, also raised questions about the interview Monday.
He quoted Guzman as saying his daughter was telling lies and he thought someone must have forced her to say such things.
"He told me, 'Poor girl, what's happening? Why is she making such unfortunate statements? That is really bad,'" the attorney said.
Gustavo Salas Chavez of the Attorney General's Office said authorities will work to confirm the identity of Guzman's alleged daughter and invite her to make a formal complaint.
Since being returned to prison after his recapture, Guzman has complained that guards do not let him sleep. His lawyers and common-law wife have given interviews in recent weeks expressing grave concern for his health.
Sales, the national security commissioner, said the security measures for Guzman are in the public interest.
"We can't forget, we always have to remember, that Joaquin Guzman Loera has profoundly harmed our society, his actions have caused the deaths of many Mexicans, he has poisoned our young people and destroyed entire families," Sales said.
Sales warned "that with this individual, his defense and some other people exists an open media strategy."
He did not take questions.
Guzman was recaptured in January in the western state of Sinaloa after fleeing a safe house through a storm sewer. He had escaped from prison in July through a mile-long tunnel.
Jose Manuel Merino of the Mexican Attorney General's Office, said the government had no official knowledge of Guzman's desire to be extradited more quickly as one of his lawyers said last week.
Merino said two formal extradition requests from the United States are being processed.