The interview came after Twitter blocked US intelligence companies from accessing a service that provides real-time information known as Dataminr after two years of cooperation.
Smith, for his part, minced no words when describing Twitter as an effective mechanism for Daesh to coordinate its activities with other terrorist groups.
"Twitter has become a cyber-sanctuary for the Islamic State (Daesh), from [the site] it is currently managing the most aggressive and ultimately effective recruitment and incitement programs, involving any terrorist group," he said.
Smith added that the problem will certainly prompt people from all across the world to be careful about communicating via social networking sites.
"Most responsible people around the world will look at this problem of the use of social media by groups like the Islamic State and al-Qaeda to recruit and incite violence as something that would necessitate that they [agree to] forgo their own privacy if they want to use social media," he said.
Meanwhile, the US intelligence community is reportedly "unhappy about the decision and [is] hoping the companies will reconsider."
Dataminr's separate 255,000-dollar contract with the US Department of Homeland Security reportedly remains in force.
Twitter's decision to end Dataminr's relationship with US intelligence community comes at a heated time: the US government seeks to expand its powers, citing national security reasons, while tech companies want to protect users' privacy.