A son of El Chapo, the jailed Mexican drug lord, pleaded not guilty to federal drug conspiracy charges on Tuesday, five days after taking a dramatic private flight across the border and surrendering himself and his father’s former business partner to U.S. officials at an airport near El Paso.

At a hearing in Federal District Court in Chicago, the son, Joaquín Guzmán López, faced an American judge for the first time since he was charged in that city last year with serving as a high-ranking member of the Sinaloa drug cartel. Included in the same indictment were his three brothers, his father and Ismael Zambada García, his father’s onetime partner in crime.

On Thursday, federal officials said, Mr. Guzmán López kidnapped Mr. Zambada García after luring him down from one of his mountain hide-outs to the Mexican city of Culiacán, which has long served as the urban stronghold for the Sinaloa cartel. After the two men's bodyguards clashed, the officials said, Mr. Guzmán López forcibly put his captive onto a private plane and flew him over the border and into the hands of U.S. federal agents.

One question raised by the cinematic abduction plot, which has gripped Mexico for days, is whether Mr. Guzmán López, who is in his late 30s, was working under any sort of deal with the U.S. agents who met — and apprehended — him and Mr. Zambada García, 76, at an airport in Santa Teresa, N.M., a 30-minute drive from El Paso.

After the hearing in Chicago, Jeffrey Lichtman, Mr. Guzmán López’s lawyer, put that question to rest, saying that his client had not reached a deal with American authorities.

“We’ve got no agreement with the government,” Mr. Lichtman said. “There has never been an agreement with the government with Joaquín Guzmán López.”