As many as 143 people are still missing after last week's attack near Moscow when gunmen sprayed concertgoers with automatic weapons and set the venue on fire, a Russian state news outlet reported on Wednesday.

The official toll from the attack on Crocus City Hall now stands at 140 dead and 182 wounded. But the state Tass news agency quoted Russia's Investigative Committee as saying that 143 more people appeared in lists compiled by the emergency services based on appeals from people about missing relatives.

In addition, the Investigative Committee said 84 bodies had been identified, including the bodies of five children.

"Molecular genetic tests are being conducted to establish the identities of the rest of the dead people," the committee said.

Maria Lvova-Belova, Russia's commissioner for children's rights, presented an award on Tuesday to a 15-year-old boy who saved more than 100 people during the attack.

The teenager worked part-time at the Crocus City Hall concert venue as a cloakroom attendant and was on duty when the shooting occurred.

The boy saw people panicking. He loudly announced that he was an employee, he knew where the exits were, and pointed the way out.

Russian Foreign Ministry spokeswoman Maria Zakharova said on Wednesday that it was "extremely hard to believe" that Islamic State would have had the capacity to launch the attack.

At a briefing with reporters, Zakharova instead doubled down on Moscow's assertions, for which it has not yet provided evidence, that Ukraine was behind the attack on the Crocus City Hall, the deadliest Russia has suffered in 20 years.

Islamic State has claimed responsibility for the massacre and United States officials said they have intelligence showing it was carried out by the network's Afghan branch, Islamic State Khorasan. Ukraine has repeatedly denied it had anything to do with the attack.

But Zakharova said the West had rushed to pin responsibility on Islamic State as a way of deflecting blame from Ukraine and the Western governments that support it.

"In order to ward off suspicions from the collective West, they urgently needed to come up with something, so they resorted to ISIS, pulled an ace out of their sleeve, and literally a few hours after the terrorist attack, the Anglo-Saxon media began disseminating precisely these versions," she said.

Russian President Vladimir Putin has said earlier the attack was carried out by extremists, but has suggested it was to Ukraine's benefit and that Kyiv may have played a role.

Meanwhile, in remarks to Russian air force pilots on Wednesday, Putin said Russia has no designs on any NATO country and will not attack Poland, the Baltic states or the Czech Republic. But if the West supplies F-16 fighters to Ukraine, they will be shot down by Russian forces.

Putin said the US-led military alliance had expanded eastward toward Russia since the 1991 fall of the Soviet Union, but that Moscow had no plans to attack a NATO state.

"We have no aggressive intentions toward these states," Putin said, according to a Kremlin transcript released on Thursday.

Putin said the F-16 could also carry nuclear weapons.

"Of course, if they will be used from airfields in third countries, they become for us legitimate targets, wherever they might be located," Putin said.

Putin's remarks followed comments earlier in the day by Ukrainian Foreign Minister Dmytro Kuleba that the aircraft should arrive in Ukraine in the coming months.

Ukraine has sought F-16s for many months. Belgium, Denmark, Norway and the Netherlands are among countries that have pledged to donate F-16s. A coalition of countries has promised to help train Ukrainian pilots in their use.