A total of 137 people were killed and 182 others were injured when a group of men in camouflage broke into the Crocus City Hall, a large concert venue in Krasnogorsk on the outskirts of Moscow, on Friday and opened fire on the crowd, according to Russian officials.
Four men, at least one a Tajik, were remanded in custody on terrorism charges, the Reuters news agency reported on Monday.
Islamic State has claimed responsibility for the attack and released what it says is footage from the attack, according to reports.
US officials said they had warned Russia of intelligence about an imminent attack earlier this month, Reuters reported.
Russian President Vladimir Putin claimed in a televised speech that some people "on the Ukrainian side" had attempted to help the attackers escape across the border from Russia, according to the Polish media.
Ukraine denies involvement
Ukraine has denied any role in the attack, and President Volodymyr Zelensky accused Putin of seeking to divert blame for the attack by mentioning Ukraine, Reuters reported.
"What happened in Moscow yesterday is obvious, and Putin and other scums are trying to shift the blame to someone else," Zelensky said on the X social media platform on Saturday.
He added: "Their methods are always the same. We have seen it all before. There were blown-up houses, mass shootings, and explosions. And they always blame others. They came to Ukraine, burned down our cities, and then tried to blame Ukraine. They torture and rape people—and then blame them.
"They have brought hundreds of thousands of their terrorists to Ukrainian territory, and they are waging war against us, but they don’t care about what happens inside their own country.
"All of this happened yesterday, and instead of taking care of his Russian citizens and addressing them, this duffer Putin remained silent for a day, thinking about how to link this to Ukraine.
"Everything is entirely predictable. Those hundreds of thousands of Russians who are now killing on Ukrainian soil would certainly be enough to deter any terrorists. And if Russians are willing to die quietly in 'crocuses' and not question their special services, Putin will try to exploit more of these situations for personal power. Terrorists must always lose."