Putin, addressing the nation, said that attackers had sought to escape towards Ukraine. He said preliminary information showed that some people on the Ukrainian side had prepared to let them cross the border from Russia.
He said March 24 would be a day of mourning.
* The United Nations Security Council on Friday condemned what it called the "heinous and cowardly terrorist attack" at a concert hall in Moscow that killed at least 115 people and wounded 145.
Islamic State, the militant group that once sought control over swathes of Iraq and Syria, claimed responsibility for the attack.
The members of the Security Council condemned "in the strongest terms the heinous and cowardly terrorist attack," said the Council in a press statement.
The Council members expressed their "deepest sympathy and condolences" to the families of the victims and the Russian people, and they wished a speedy and full recovery to those who were injured.
They reaffirmed that terrorism in all its forms and manifestations constitutes "one of the most serious threats" to international peace and security.
The Council underlined the need "to hold perpetrators, organizers, financiers and sponsors of these reprehensible acts of terrorism accountable and bring them to justice.
It urged all states to cooperate with Russia and other relevant authorities. The Council reiterated that any acts of terrorism are criminal and unjustifiable, regardless of their motivation, wherever, whenever and by whomsoever committed.
It reaffirmed the need for all states to combat threats to international peace and security caused by terrorist acts.
* World leaders denounced the terrorist attack claimed by the Islamic State that left at least 115 people dead and over 140 injured in a Moscow concert hall on Friday. They express their solidarity with the victims, their loved ones and all the Russian people.
* Russia has arrested 11 people including four suspected gunmen in connection with the shooting rampage in a concert hall near Moscow, the Kremlin said on Saturday.
Russian Security Council Secretary Nikolai Patrushev, a top ally of President Vladimir Putin, said on Saturday that those responsible for the concert attack near Moscow would be punished, the TASS state news agency reported.
Patrushev said the attack showed just what a threat terrorism was to Russia.
* Ukraine was not involved in Friday's shooting attack near Moscow and suggestions of a Ukrainian link "have nothing in common with reality," a spokesman for Kyiv's military spy agency said on Saturday.
