"Intelligence should keep a tab on all (except relatives and friends) who assembled before Memon's corpse. Many are potential terrorists," Roy tweeted.
The governor, who faced criticism for his remarks, also tweeted, "It is my constitutional duty to bring matter of public interests to public notice. My position as governor is not thereby compromised."
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Later, talking to a TV news channel here, Roy said that he has excluded Memon's relatives and friends. "Why did others come to see a man who was hanged. They must have sympathy for him."
Roy also said in his tweet, "When I suggested intelligence keeping a tab, I mentioned no community."
Criticising Roy, former Lok Sabha Speaker Somnath Chatterjee said he occupies a constitutional post and his comments were not in line with the Constitution.
"He should not have resorted to Twitter if he wants to give any advise to the government. He could have told the chief minister (of the state) or he could have sent a message to him," Chatterjee said.
Senior Trinamool Congress leader and state minister Subrata Mukherjee said Roy should remember that he is occupying a constitutional position.
"He should be immediately dropped without any futher delay. I am saying this as a citizen of the country," Mukherjee added.