India hanged Kasab, 25, who was pronounced guilty for the bloody rampage that killed 166 people and injured 300 others, Wednesday morning.
The Pakistani arm of the Taliban said Wednesday that Kasab was a hero for the jihadis and his death was a great loss, according to a Reuters report.
A Taliban spokesman said that they would avenge the "killing of Kasab" by striking at Indian targets.
"We have decided to target Indians to avenge the killing," said spokesman Ehsanullah Ehsan over telephone from an undisclosed location, Reuters reported.
The group also demanded that Kasab’s body be returned to the Taliban or to his family.
"If they don't return his body to us or his family we will capture Indians and will not return their bodies," he said. The group said that his death would encourage more people to be martyrs for the cause of Islam.
India claims to have completed all due legal process for the execution and had reportedly informed his country and family in advance about the hanging. Indian Foreign Minister Salman Khurshid said that the country was ready to consider handing over Kasab’s body to Pakistan or his family if such a request was made.
"We also had in our possession a particular address given by Kasab and we did convey to that address as well the decision that had been taken," he said.
However, in the absence of any communication from Pakistan, Kasab was buried in a pit on the premises of the Pune's Yerawada Central Jail, where he was hanged in complete secrecy.
People in Kasab’s village in Pakistan reportedly expressed anger over his death and also demanded that his body be handed over to them.
However, Pakistan, which has not yet accepted Kasab's citizenship, has not asked for his body or even acknowledged receiving any communication on the issue from the Indian government.
A Times of India report said he had sought forgiveness from God just before being hanged.
"Allah qasam maaf karna, aisi galti dobara nahi hogi' (I swear by Allah, please forgive me, such a mistake won't be repeated)," were reportedly Kasab's final words.