A federal judge in Brooklyn dismissed claims on Friday that Joaquín Guzmán Loera, the Mexican drug lord best known as El Chapo, had been improperly extradited to the United States from Mexico, handing the defendant the latest in a string of legal defeats.

Last month, Mr. Guzmán’s public defenders filed a motion claiming that the federal government had brought Mr. Guzmán to Brooklyn for prosecution, even though his original extradition agreement with Mexico called for him to be tried in either California or Texas. Federal prosecutors countered that on Jan. 19, the day that Mr. Guzmán was placed on a Mexican jet and flown to New York, the Mexican government issued a waiver to what is known as the Rule of Specialty, which requires a government to hew to the specifics of an extradition agreement.

But in his order on Friday, Judge Brian M. Cogan of United States District Court for the Eastern District of New York cited a New York appeals court ruling from this year that said defendants who are extradited to the United States have no legal standing to question whether the Rule of Specialty applied. Judge Cogan’s order means that the sprawling international drug case can continue moving forward. A trial has been scheduled for April.

“We’re not surprised by the court’s decision given the state of the law,” said one of Mr. Guzmán’s recently hired private lawyers, A. Eduardo Balarezo. “However, we do believe that Mr. Guzmán’s extradition to New York was improper.”