Earlier in the day, Headley testified in the Mumbai court through a video conference from an undisclosed location in the United States.
"Before the Mumbai attack in 2008, Lashkar tried to attack Mumbai twice but the plan failed as all the arms and ammunition sank in the sea as the boat struck on the rocky surface. The same group succeed in third time," Ujjwal Nikam told reporters.
According to the prosecutor, Headley, who first confessed his involvement in the attacks in 2010, said he had used a false identity at the behest of his "handler" Sajid Mir, an LeT operative.
Headley also said he had long been an LeT true follower, which he joined in 2002, and changed his name to come to India. He also added that he had visited Mumbai at least seven times, before and after the attacks.
Indian Minister of State for Home Affairs Kiren Rijiju told reporters that Headley's confession "will lead us to a logical conclusion of the whole case."
The US citizen is the first foreign national to testify in India in a terror case.
Headley was arrested by US authorities in 2013 and sentenced to 35 years in jail.