(CNN) -- Sinaloa cartel boss Joaquin "El Chapo" Guzman will face charges in Mexico before any possibility of extradition, Mexico's ambassador to the United States said Tuesday.
"Mr. Guzman still has pending time to serve in Mexico from his original sentence and he also faces new charges in Mexico that will be processed in Mexican federal courts," Ambassador Eduardo Medina-Mora said in a statement. "If and when we receive an extradition request, it will be analyzed by the appropriate Mexican legal authorities and if granted, Mexico will decide upon the right moment to execute that possible extradition request."
The ambassador's statement came on the same day that U.S. Attorney General Eric Holder called his counterpart in Mexico to congratulate him on Guzman's capture, according to the Justice Department.
Also Tuesday, federal prosecutors in New York unveiled the latest indictment naming Guzman, alleging drug trafficking and money laundering. There are at least seven indictments against Guzman in various U.S. jurisdictions, and at least one U.S. attorney's office has said it plans to seek extradition.
"Bilateral security and justice cooperation between Mexico and the United States unfolds in a mature and serene way, and cases like Mr. Guzman's are processed with openness. I think that the charges he faces in Mexico will be processed first and an eventual extradition request would be considered at the appropriate time," Medina-Mora said. "Mr. Guzman could eventually face the charges against him in the U.S., after facing the charges against him in Mexico."
When Guzman escaped from a Mexican prison in 2001, he had served seven years of a 20-year, nine-month sentence.
There were eight warrants for Guzman's arrest when authorities captured him over the weekend: two tied to his 2001 escape, and six more for alleged crimes committed since then, Mexico's attorney general's office said.
Guzman's attorneys have already filed a motion to block his extradition.
Rep. Michael McCaul, chairman of the House Homeland Security Committee, said Sunday that Mexican officials should consider extradition now.
"The normal sequence is Mexico, being a sovereign nation, has the first prosecution. However, there's a history here. He escaped from a prison in 2001. There is corruption in that country. And I would ask that the Mexicans consider extraditing him to the United States, where he will be put into a 'supermax' prison under tight security, where he cannot escape, and be brought to justice with a life sentence," McCaul told ABC's "This Week."
"I think that would be the best course of action for not only Mexico, but also the United States, in ensuring that what happened in 2001 does not happen again."
CNN's Catherine E. Shoichet and CNNMexico's Rodrigo Aguiar contributed to this report.