News agencies reported that Kasab admitted that he hailed from the village of Faridkot in Pakistan's eastern province of Punjab.
More than 170 people were killed during a three-day rampage through India's commercial capital last November.
Police say Kasab was one of 10 heavily armed men who arrived in Mumbai by sea before attacking five-star hotels, the main train station and a Jewish centre.
"He had earlier requested legal assistance from Pakistan. We need some more time to appoint a lawyer to defend him," Ujjwal Nikam, a public prosecutor, said.
Two Indians - Faheem Ansari and Sabahuddin Ahmed - who are accused of being part of Lashkar-e-Taiba, the group blamed for the attacks, were also appearing at the trial through the video link.
Al Jazeera's Matt McClure, reporting from Delhi, said Kasab was appearing in court from his cell via video link because "an elaborate $400,000 tunnel linking the court and the prison house being built purposely for the trial is yet to be completed".
"This is the formal start to the trial ... but it is also a small part of a larger diplomatic prosecution by Indian authorities of Pakistan before the international community trying to show that their nuclear neighbour is, as India says, part of the global epicentre of terror."
The attacks have strained already poor relations between the two nuclear-armed neighbours.
Kasab told investigators that the assault was planned in neighbouring Pakistan and carried out by Pakistanis, Indian officials say.
India has accused state agencies of complicity in the attack, an allegation that Islamabad denies.
Police in Pakistan have detained a number of people in connection with the attacks and banned a group suspected of having links to Lashkar-e-Taiba.
The case will be heard again on March 30.