Russia lowered flags to half-mast on Sunday for a day of mourning after scores of people were gunned down at a rock concert near Moscow in the deadliest attack inside the country in decades.

Russian President Vladimir Putin declared a national day of mourning after pledging to track down and punish all those behind the attack, which left 133 people dead, including three children, and more than 150 injured.

"I express my deep, sincere condolences to all those who lost their loved ones," Putin said in an address to the nation on Saturday, his first public comments on the attack. "The whole country and our entire people are grieving with you."

Islamic State (ISIS) has claimed responsibility, but Russian officials said the claim has not been verified. Putin has said the attackers had been trying to escape to Ukraine and he asserted that some on "the Ukrainian side" had prepared to spirit them across the border.

Ukraine has repeatedly denied any role in the attack, which Putin also blamed on "international terrorism."

People laid flowers at Crocus City Hall, the 6,200-seat concert hall outside Moscow where four armed men burst in on Friday just before Soviet-era rock group Picnic was to perform its hit "Afraid of Nothing".

The men fired their automatic weapons in short bursts at terrified civilians who fell screaming in a hail of bullets. It was the deadliest attack on Russian territory since the 2004 Beslan school siege.

Long lines formed in Moscow on Saturday to donate blood, and in the southwestern city of Voronezh, people laid flowers and lit candles at a monument to children who died there in a World War II bombing, in solidarity with those who died in the attack near Moscow.

"We, like the whole country, are with you," the governor of the Voronezh region, Alexander Gusev, said on the Telegram messaging app.

Russia's Federal Security Service (FSB) revealed on Saturday that 11 individuals connected to the attack were apprehended, including four direct perpetrators, noting that the gunmen had contacts in Ukraine and were captured near the border.

"They tried to hide and moved towards Ukraine, where, according to preliminary data, a window was prepared for them on the Ukrainian side to cross the state border," Putin said.

In video footage published by Russian media and Telegram channels with close ties to the Kremlin, one of the suspects said he was offered money to carry out the attack.

"I shot people," the suspect, his hands tied and his hair held by an interrogator, a black boot beneath his chin, said in poor and highly accented Russian.

When asked why, he said: "For money." The man said he had been promised half a million roubles (a little over $5,000). One was shown answering questions through a Tajik translator.

(With input from agencies)