President Vladimir Putin on Monday acknowledged for the first time that "radical Islamists" were behind last week's attack on a concert hall outside Moscow, but suggested Ukraine was somehow involved.

Eleven people have been detained in connection with the attack, which saw camouflaged gunmen storm into Crocus City Hall, open fire on concert-goers and set the building ablaze, killing at least 137 people.

"We know that the crime was committed by the hands of radical Islamists, whose ideology the Islamic world itself has been fighting for centuries," Putin said in a televised meeting.

"This atrocity may be just a link in a whole series of attempts by those who have been at war with our country since 2014 with the hands of the neo-Nazi Kyiv regime," he said, referring to Ukraine.

"Of course, it is necessary to answer the question, why after committing the crime the terrorists tried to go to Ukraine? Who was waiting for them there?" Putin asked.

Islamic State jihadists have said several times since Friday that they were responsible, and IS-affiliated media channels have published graphic videos of the gunmen inside the venue.