Mr. Maduro and his wife Cilia Flores have been detained in a prison in Brooklyn since the US deployed military forces to arrest and take him to the US.
According to records, Mr. Maduro smiled when entering the courtroom and did not speak throughout the trial.
Outside the Manhattan courthouse, supporters and opponents of Mr. Maduro gathered, blew horns, beat drums and rung bells.
The hearing on March 26 focused on the ongoing debate about who would pay the legal costs for Mr. Maduro and his wife.
The administration of President Donald Trump said that the current US sanctions do not allow the Venezuelan government to pay these fees.
Meanwhile, Mr. Maduro and Ms. Flores argued that they did not have enough personal finances to pay for their own defense.
I will not reject this case," Judge Alvin Hellerstein said in response to a request from Mr. Maduro's lawyer.
Judge Hellerstein also reminded US officials of the legal basis for preventing the Venezuelan government from paying this fee.
The most important goal and need today, as well as constitutional rights, is the right to be defended," he added.
The judge has not yet issued a final ruling on this issue and it is still unclear when the decision will be issued.
Mr. Maduro is facing charges including: "drug terrorism" plot, cocaine import plot, possession of machine guns and destructive equipment, and plot to possess these weapons. Mr. Maduro has denied the charges.
Meanwhile, President Trump declared "there will be other cases brought up" against Mr. Maduro, but did not elaborate.
