"He has, however, not admitted to all of the 86 charges framed against him."
The judge said Kasab's confession would be kept on record and considered by the court "at an appropriate stage".
Kasab told the court on Monday that he was one of the armed men involved in the attacks in which 166 people were killed and more than 300 others were wounded.
He said he had orders to take hostages at Mumbai's main railway station where he and an accomplice opened fire and threw grenades, killing 52 people and injuring more than 100 others.
The rail station attack was the bloodiest episode of the 60-hour reign of terror against multiple targets in south Mumbai.
Other targets included two luxury hotels and a Jewish centre.
If found guilty, Kasab could face the death penalty.
The court had delayed a decision on whether to accept his confession, after prosecutors said Kasab's statement was incomplete and accused him of using the confession to seek clemency.
Kasab, who had originally pleaded not guilty to the charges, said that he had not confessed to avoid the death penalty and was willing to be hanged for his actions.
"Please go ahead and hang me," Kasab said.
It was not immediately clear what prompted him to change his plea.
The Mumbai attack severely strained relations between India and Pakistan, halting peace initiatives between the nuclear-armed rivals.
India claims that armed groups in neighbouring Pakistan were behind the well-planned attack and that Islamabad is not doing enough to clamp down on them.
Though Islamabad has denied state involvement in the attack, it has promised to act against individuals suspected to be involved.