“We think the process was fine during the trial, but not during post-conviction,” Oren Yaniv, a spokesman for the district attorney, said.

It is yet another blow to the work of the office under Mr. Hynes, who was the Brooklyn district attorney for 23 years before losing the elected position to Mr. Thompson in 2013.

The issue was whether a witness in the 1993 trial had come forward on his own, as the prosecution claimed, or whether prosecutors had used a material-witness order to detain the witness in a hotel room until he agreed to testify. During the trial, and in post-conviction arguments in the early to mid-2000s, prosecutors denied there was any such order. But there was, and in recent days it emerged that the prosecution had known about the order even as it asserted otherwise.

The discovery of a 2004 email acknowledging the material-witness order led prosecutors to abandon their defense of the conviction, a prosecutor, Matthew Stewart, said in court on Monday.

In a statement, Mr. Thompson said: “Due to what we have uncovered, we will not continue with the hearing because to do so would be unfair to Mr. Quezada. Since we can’t try this case, we will no longer object to his release.”