Authorities reported at least 50 people had been injured and 14 people were killed after an explosion between two underground metro stations in Russia's second-largest city on Monday.
Prime Minister Dmitry Medvedev described the blast as a "terrorist attack." Although, an anti-terror investigation has been initiated, other potential causes are also being investigated.
The suspected suicide bomber is believed to have been a Kyrgyzstan native who had later obtained Russian citizenship, the central Asian country's security service said on Tuesday.
"The Kremlin has experienced two unexpected and jarring incidents in just over a week, and this could lead to action against dissent that is stronger than it would otherwise be," Eurasia Group analysts said in a note.
"Such action would add to U.S. and European governments' criticisms of the arrests that followed the 26 March protests."
Putin witnessed one of the largest outbreaks of anti-government demonstrations in years when protestors campaigned against corruption throughout the country in late March.
The Kremlin detained several hundred protestors in connection with the unsanctioned rallies, including Putin's political rival, Alexei Navalny. Several Western countries urged Moscow to release those who had been arrested and sentenced to jail, including Navalny.
"The regime is terribly tough, so (there is) no need for more measures," Andrei Kolesnikov, senior associate at the Carnegie Moscow Center, told CNBC via email.
Kolesnikov said it is likely that the only major consequence from Monday's subway attack would be additional police enforcement in an effort to prevent further incidents.
Putin, who is widely expected to run for what would be his fourth consecutive term next March, stressed that dissenters must respect the law or face the consequences.
"Everybody should act in political processes within the framework of the law. All those who go outside this law should bear punishment in accordance with Russian law," Putin told CNBC via an interpreter in an interview at the International Arctic Forum in Arkhangelsk on Thursday.
The Russian premier, who was in St. Petersburg at the time of the attack, was pictured laying a floral tribute to the victims of the bomb blast on Monday evening.