Assailants had been "in contact" with people in Ukraine, FSB said.
Russian President Vladimir Putin on Saturday called an attack on a concert hall that killed more than 100 a "barbaric terrorist act" and vowed harsh retribution to all those involved.
In a televised address, Putin said all four gunmen had been arrested before they had a chance to cross the border into Ukraine.
"I am speaking to you today in connection with the bloody, barbaric terrorist act, the victims of which were dozens of innocent, peaceful people," Putin said in his first public remarks since the attack.
"All four perpetrators of the terrorist attack who shot and killed people have been detained. They were travelling towards Ukraine where, according to preliminary information, they had a window to cross the border," the Kremlin leader said.
Russia's FSB security service said earlier the assailants had been "in contact" with people in Ukraine as they tried to flee the country.
At least 115 people were killed by armed gunmen at the Crocus City Hall in a suburb on the northern edge of Moscow on Friday. The concert hall was set ablaze. The attack has been claimed by the Islamic State group but Russian authorities have not mentioned this.
"Terrorists, murderers, non-humans will face the unenviable fate of retribution and oblivion," said Putin, who declared Sunday a day of national mourning across Russia.
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