Interior Minister Miguel Angel Osorio Chong said guards who monitored the surveillance cameras inside Guzman's cell "immediately" sounded the alarm when they noticed that "he was no longer there".
"The arrival of guards (in the cell) took place 18 minutes later," Osorio Chong said after he and other law enforcement officials met with Congress's security committee to discuss the escape.
Prosecutors are investigating whether the prison's protocols were properly followed, he said, adding that the Altiplano prison some 90 kilometers west of Mexico City was placed on lockdown after the escape and that authorities went through the tunnel.
Closed-circuit camera footage released by the government this week showed that Guzman paced in his cell before bending down behind a short partition wall in the shower.
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The Sinaloa cartel chief then rode on a motorcycle with two carts rigged on a rail system inside a 1.5 kilometer tunnel built for his second escape in 14 years.
The 18 minutes it took for guards to enter his cell gave him a big head start.
Guzman escaped only 17 months after Mexican marines captured him in February 2014 in the Sinaloa state resort of Mazatlan with the help of US law enforcement agencies.
Attorney General Arely Gomez told the lawmakers that Mexico formally received a US extradition request for Guzman on June 25, some two weeks before his escape, her office said in a statement.
Gomez instructed prosecutors to analyze the request after it was received, the statement said.
Mexican authorities have come under fire for failing to keep the nation's most powerful drug kingpin in prison, raising questions about why it never extradited him to the US, where prisons are deemed more secure.