Ihsanullah Ihsan said Thursday his group would seek to avenge Wednesday's hanging in India of Mohammed Ajmal Amir Kasab, but gave no details, CNN reported.
The Times of India quoted the Taliban spokesman as saying his group would strike Indian targets anywhere.
The Pakistani Taliban is known locally as the Tehrik-i-Taliban Pakistan. While different from the Taliban in Afghanistan, the Pakistani group has connections with the former as well al-Qaida.
Kasab, 24, the lone survivor of the Pakistani group that staged the deadly attacks in India's financial capital, was executed in India's western Pune city, the Indian Home Ministry said. In its announcement, the ministry said the execution took place after Kasab's clemency petition to the Indian president has been turned down.
Kasab's execution came after a four-year-long legal trial and after the Indian Supreme Court had upheld his death sentence. He was the lone survivor among the 10 gunmen involved in the November 2008 attacks at various locations Mumbai that lasted three days and left 166 people dead, including foreigners, and more than 200 wounded. The other gunmen were killed by security forces during the siege.
All the 10 gunmen were reported to have reached Mumbai by sea from Karachi, Pakistan.
CNN quoted an official of the Indian Foreign Ministry as saying Pakistan had been asked to provide additional protection for the Indian diplomatic staff. It said the official had no immediate comment on the Taliban threat.
CNN said the Taliban spokesman also demanded that Kasab's body be returned to Pakistan for an Islamic burial.
In announcing Kasab's hanging, the Indian government had said his family and the Pakistani Embassy had been informed, and that he was buried in the premises of the jail where the hanging took place. Various media reports said there had been no claim for the body from Pakistan.
CNN said the Pakistani Foreign Ministry declined to respond to the Taliban criticism that the government had not asked for the return of Kasab's body.