The Kremlin said Saturday that President Vladimir Putin was still pained by last week's massacre at a Moscow concert hall, even if this was not outwardly visible.

More than one week after gunmen stormed Crocus City Hall on the outskirts of the capital, killing 144 people and injuring hundreds more, Putin has not publicly met with survivors or visited the scene of the attack.

This is despite Russian media reporting that Western diplomats, including those from the European Union and United States, visited a makeshift memorial for victims outside the venue on Saturday.

Spokesman Dmitry Peskov told a state TV reporter that Putin was dealing with the tragedy in his own way.

"Believe me, if you don't see tears on his face, it doesn't mean he's not in pain. And what he is going through, it is unlikely that anyone will ever recognise and understand," he said.

The Kremlin gave no indication this week the Russian leader plans to visit the relatives of those killed in the attack, the country's deadliest in two decades.

Instead, security agencies have shifted the focus on to who was responsible, detaining a dozen suspects including the four alleged assailants from Tajikistan.

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

While Putin has acknowledged "radical Islamists" carried out the carnage, he has continued to allege arch-foe Ukraine was involved somehow, without providing any evidence.