One week after Russia's deadliest terror attack in two decades, mourners outside Crocus City Hall expressed a mixture of grief, condolences for the dead and anger.

Russian rock band Piknik was moments away from performing last Friday when gunmen stormed the venue, opened fire and set it ablaze, killing at least 143 people.

Amid the grief and confusion, the Kremlin has acknowledged "radical Islamists" carried out the carnage, arresting 12 people including the four alleged attackers from Tajikistan.

But it has directed much of its anger at arch-foe Ukraine. It insists that Kyiv was intimately involved in the attack, despite having provided no evidence.

A few paces from the burnt-out building where rescuers had been searching for bodies days before, a mound of flowers, hand-written notes and toys continues to grow.

"Surely someone from Ukraine, some Ukrainian oligarch is behind this," a man outside the concert hall told AFP.

"The perpetrators were Tajiks," a woman nearby said, "but I'm sure the one who ordered it is Ukraine."

Kyiv and its Western allies have dismissed as absurd accusations that Kyiv was involved.

The United States warned weeks before the massacre it was monitoring reports extremists planned to attack mass gatherings, including concerts.

But the Kremlin has pushed back at suggestions it was warned in advance, expressing full confidence in its security services, despite criticism over their failure to thwart the attack.

- 'Pray for the dead' -

The massacre has also re-ignited a debate about re-introducing the death penalty, an idea that has found sympathy among some hardline Russian lawmakers.

"I am in favour of introducing the death penalty in such situations," said Katerina, a 29-year-old restaurant worker.

"Everyone would be accountable to God," she said.

A priest at the St. Nicholas Church, an unassuming Orthodox building overlooking the concert hall, struck a more conciliatory tone.

"Be attentive to yourself and to your loved ones," he said.

"The most important thing is to love each other. When we live in love, it is easier."

When asked whom he thought was behind the attack, he answered: "I don't know."

Varvara Nikitina, a 33-year-old housewife, said she was there to "pray for the dead".

"I came here today to do my duty," she told AFP.

Kremlin spokesman Dmitry Peskov has given no indication President Vladimir Putin plans to visit the family members of those killed or go the scene of the massacre.

The Russian leader was seen lighting a candle for the victims at a Moscow church last week, but has not visited the scene of the attack or publicly met with any victims.

"If any contacts are necessary, we will inform you accordingly," Peskov said, when asked if Putin planned to meet families of the dead.