India's interior ministry issued a statement urging citizens to avoid crowded places on Monday, while police have increased patrols throughout the city.
Kasab was allegedly arrested in a stolen car at a roadblock shortly after the attacks.
Prosecutors presented a range of evidence during his seven-month trial, including fingerprints, DNA evidence, security camera footage and photographs allegedly showing Kasab carrying an assault rifle.
Kasab first denied the charges, then pleaded guilty, before reversing his guilty plea, claiming he was set up by police.
M.L. Tahaliyani, the judge presiding over the case, has spent more than a month reviewing the evidence. He said in March that he planned to issue a verdict on May 3.
Two Indians, accused of providing the attackers with maps of Mumbai, are also on trial.
Thirty-five other people have been named as "co-conspirators" in the case. Seven of them, including a founder of the Pakistan-based group Lashkar-e-Taiba, are currently on trial in Pakistan. India blames the group for masterminding the attacks.
The Pakistani government last month asked India to hand over Kasab and one of his co-defendants, but the Indian government has not responded to the request.