"If there is a threat to the life and wellbeing of our employees...liquidate the bandits," the president said.
Russia's security service posted images and video of an apartment they said served as a "laboratory" of arms for the detained extremists.
The drill will help authorities practice their response to a terrorist threat in the middle of Moscow.
Convicted terrorists can go to jail but those that recruited them deserve harsher sentences and "could be shot," Chechnya's leader said.
The deadly stabbing attack in Dagestan follows a similar incident in Siberia that left eight people injured, according to reports.
Monday's bombing in St. Petersburg followed a long history of militant attacks on Russia under President Vladimir Putin.
Shots and two explosions were reported in St Petersburg Wednesday morning.
A police station in Stavropol region was attacked on Monday morning.
The Kremlin has refused to speculate on the culprits behind the attack.
Over 3,500 bank accounts were frozen in 2015, the head of Rosfinmonitoring told Vladimir Putin.
The group urges militants from the Caucasus to plan attacks and start a land grab.
Gulchehra Bobokulova has confessed to the killing and said she acted in protest over the bombing of Syria.
Sources in law enforcement are blaming a suicide bomber, but those reports are unconfirmed.
The group has been in the region since the start of the conflict, a Chechen government source said.
The FSB reported having arrested seven ISIS affiliates who were planning to attack Moscow and St. Petersburg.
The man was reportedly plotting attacks in Chechnya and Dagestan.