Tehreek-i-Taliban Pakistan (TTP) spokesman Ehsanullah Ehsan had said that the outfit would mount attacks "in India and anywhere" to avenge the hanging of Kasab.
Police said there would be heavy security deployment in and around the city. Vital organisations, including the airports, Bhabha Atomic Research Centre (BARC) and others will be under tight vigil and extra security would be deployed there, police said.
"We will also check the entry and exit points of the city," a police official said.
Security would be stepped up at public places like the railway stations and bus stops, he said.
Police will also conduct "nakabandi" at all important places in the city.