Ukraine has rejected accusations it was involved as absurd.
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 they were linked to Ukraine somehow.
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 139 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.
But the Russian leader said "many questions" remained unanswered, including why the attackers tried to flee to Ukraine -- a claim that Kyiv has rejected.
"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.
"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," he said, referring to Ukraine and its allies.
Ukraine has rejected accusations it was involved as absurd.
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.
When asked about IS's claimed involvement, Kremlin spokesman Dmitry Peskov said on Monday that an investigation was still ongoing.
Officials expect the death toll to rise further, as rescuers were searching the site for remains on Monday and 97 are still in hospital.
- Suspects in court -
The Kremlin has expressed confidence in the country's powerful security agencies, despite swirling questions over how they failed to thwart the massacre amid public and private warnings by the United States' intelligence apparatus.
In a series of late-night hearings in Moscow that ran into the early hours of Monday, four of the suspects -- with bruises and cuts on their swollen faces -- were dragged in to the capital's Basmanny district court before dozens of reporters.
FSB officers wheeled one into the hearing on a gurney, his eyes barely open.
Peskov refused to comment on reports and videos on social media that showed bloody interrogations of the suspects after they were arrested on Saturday.
The court identified them as Muhammadsobir Fayzov, Shamsidin Fariduni, Rachabalizoda Saidakrami and Dalerjon Mirzoyev.
Russian state media said they were all citizens of Tajikistan.
Two of them pled guilty, the court said.
Three other suspects, whom Russian media identified as family members Aminchon Islomov, Dilovar Islomov and Isroil Islomov, were remanded in pre-trial detention on Monday.
One of those detained has Russian citizenship, the Interfax news agency reported.
All of those held in custody have been charged with terrorism and face up to life in prison. The Kremlin has pushed back at suggestions the death penalty will be re-introduced.
- Removing rubble -
At least 139 people died in the attack, according to Alexander Bastrykin, head of Russia's Investigative Committee.
After walking through the theatre shooting spectators, the gunmen set fire to the building, trapping many inside.
Victims died both of gunshot wounds and smoke inhalation, according to Russia's Investigative Committee.
More than 5,000 people were in the concert hall when the gunmen stormed in ahead of a sold-out rock concert, Russian state media cited a spokesperson from the venue owner as saying Monday.
Rescuers will continue sifting through the rubble and clearing debris at the site until Tuesday evening, said Andrey Vorobyov, governor of the Moscow region.
"The task is to remove the rubble to make sure there are no bodies underneath," Vorobyov said in a Telegram post.
Putin asked his security forces again on Monday to "identify all those involved in the terrorist act", including its "orderers".
"Despite our universal pain and sorrow, compassion and legitimate desire to punish all the perpetrators of this atrocity, the investigation must be conducted in the highest degree of professionalism, objectivity, without any political bias," Putin said.
- Mourning -
The FSB has said the gunmen had "contacts" in Ukraine, without providing more details.
Ukrainian President Volodymyr Zelensky has denied any Ukrainian involvement.
The United States, which on March 7 warned about an "imminent" attack in Moscow by "extremists", has said IS bears "sole responsibility".
On Monday, French President Emmanuel Macron warned Russia against "exploiting" the attack to blame Kyiv.
Russia observed a day of national mourning on Sunday, with dozens coming to lay flowers at a memorial to the victims, and tribute posters were erected on the sides of buildings and at transport stops across the country.
Russian schools were holding special lessons on "terrorism," on Monday, with children wearing white ribbons in honour of the victims, state TV presenters said in a news bulletin.
Tajikistan's President Emomali Rahmon condemned the attack again on Monday, after Russian media reported the gunmen were Tajik citizens.
The attack "calls on all of us, especially parents, to once again pay even more serious attention to the education of children," he was quoted by Russian news agencies as saying.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
