Guzman, who is being held in Lower Manhattan, is typically on 23-hour lockdown. His defense is restricted to two federal defenders and two approved paralegals who can see their client in jail. The prison must know who is present in the federal defender's office during conference calls.
On Friday, defense attorneys sought to relax some of the security measures surrounding Guzman's incarceration.
"We think it's ridiculous that the government expects Mr. Guzman to choose a counsel when he is locked up 23 hours a day," Defense attorney Michael Schneider said.
Judge Brian Cogan responded to the defense's request, saying, "They're taking extra security measures. I think we all know the reasons for that." He said he would defer to prison officials and the marshals.
Guzman has repeatedly been imprisoned and escaped in Mexico. U.S. authorities pursued him for years. To get Mexico to hand him over to the U.S., prosecutors agreed not to seek the death penalty. They're demanding he forfeit $14 billion in assets.
Guzman's wife, former teen beauty queen Emma Coronel, was in court, and the defense also asked for permission for her to visit Guzman, but the judge again deferred to prison officials who have said no.
The case was designated complex with tens of thousands of documents and thousands of hours of wiretap recordings. Prosecutors are urging tight security around the materials, but the defense said restrictions on evidence were "over broad."
Attorneys questioned El Chapo's extradition to New York since paperwork mentioned only the charges brought against him in Texas and California. They suggested they may seek a venue change.
Prosecutors questioned whether Guzman is entitled to a taxpayer-funded defense since he has access to "substantial assets," but the defense said he has no way to hire a lawyer. Cogan responded that his family could hire for him.
A judge initially ruled that Guzman would appear in court by video on Friday rather than have marshals escort him to and from a high-security Manhattan jail cell. The order was changed after his lawyers asked the judge to reconsider.
WATCH: Video of "El Chapo" leaving Manhattan for Brooklyn court:
On Friday morning, Guzman was taken from jail in Lower Manhattan to federal court in downtown Brooklyn in a 12-car caravan that shut down the outbound Brooklyn Bridge for 15 minutes.
He is charged with running a massive drug trafficking operation that laundered billions of dollars, and oversaw murders and kidnappings. He has pleaded not guilty.
The next hearing is in May.
The Associated Press contributed to this report.