In 2005, when Zambada said the first payoff occurred, García Luna was in charge of the Federal Investigation Agency, Mexico's federal police force. The following year, when he was accused of taking a second bribe, García Luna had been appointed the country's secretary for public security.

Garcia Luna, in a written statement, said the accusations were "defamation" and "perjury" and made without any proof.

Zambada also told the jury about another multimillion-dollar bribe he paid in 2005. That one, he said, went to a top security official who had worked under Mexico's president-elect, Andrés Manuel Lopéz Obrador, when Lopéz Obrador was the mayor of Mexico City.

A spokesman for Lopez Obrador did not immediately respond to a call and text message seeking comment.

If true, the testimony suggests that cartel bagmen had access to the highest levels of Mexico's government and criminal-justice system.

Zambada Garcia has spent four days spilling the cartel's secrets as a witness in the US federal government's case against Guzman.

Zambada gave his testimony about the bribes on the fifth day of trial under cross-examination by one of Guzman's lawyers, William Purpura. Guzman's lawyers are trying to persuade jurors that Guzman was the innocent victim of a conspiracy by American drug agents and Mexican government officials to set him up.

While Zambada has figured heavily in the prosecution's case so far, his brother, Ismael Zambada García, who is still at large, and whom the defence alleges ordered the bribes to be paid, has been central to the Guzman's defence.

Ismael Zambada, known as Mayo, was Guzmán's longtime partner in the Sinaloa cartel. The defence contends that it was him who actually controlled the cartel, and that he had for years framed Guzmán with the help of American drug agents and corrupt Mexican politicians, including two of the country's presidents.

Guzman, 61, is charged with 17 criminal counts and faces life in prison if he is convicted. He was extradited to the United States in January 2017, after twice escaping Mexican prisons.

Zambada, who was called to testify against Guzman under an agreement with US prosecutors, previously told jurors that his brother and Guzman worked together for years to move multi-tonne shipments of cocaine from Colombia through Mexico into the United States, while arranging for their rivals to be murdered.

The courtroom audience was waiting for more details about paying off a Mexican president-elect, after an off-record discussion last week revealed that Zambada had previously told the authorities that he had paid "the now incumbent president of Mexico" at least $US6 million in bribes.

The defence asked for permission to bring that information out in open court, but Judge Brian M. Cogan has been unwilling to entertain that line of questioning.

Hours before Zambada appeared for his final day of testimony, prosecutors filed a motion under seal "to preclude cross-examination." The secret motion prompted a lengthy discussion out of the jury's hearing on Tuesday afternoon, the transcript of which was also sealed.

After that discussion, Judge Cogan announced he was going to limit the questions that Guzmán's lawyers could ask Zambada, saying the value of the information did not outweigh, as he put it, "protecting individuals and entities who are not parties to this case and who would face embarrassment".

When Zambada took the stand again to finish his testimony, Guzmán's lawyers were only allowed to ask vague questions about bribes to presidents. William Purpura, one of the Guzmán's lawyers, asked Zambada, for example, if he would "corrupt the president of Mexico" if he could.

"Perhaps," Zambada responded.

The prosecution is expected to introduce 15 more cooperating witnesses who, like Zambada, will offer an inside view of Guzmán and the cartel's operations.