|This is the first attack on a concert|
A government minister told reporters at the scene that 20 people were injured.
"Two explosions occurred. These were two women suicide bombers. As a result, 16 people have died. This does not include the suicide bombers. Twenty people have been taken to hospitals with injuries," said Boris Gryzlov.
Government ministers are blaming Chechen rebels.
Gryzlov said government plans to hold a Kremlin-run local presidential election in Chechnya, announced a day earlier may have instigated the latest attack.
Putin had issued a decree on Friday ordering a local presidential election to be held in Chechnya on 5 October.
"I presume that this inhumane situation, this terrorist act, is linked with the staging of this event," Gryzlov said.
If it was carried out by Chechens, the suicide attack would be a new instance of a tactic used by the region's rebel fighters, including several women, only relatively recently in their decade-old campaign to break from Moscow's control.
The women had apparently been prevented from entering the site and blew themselves up outside admission booths at Tushino airfield, where thousands had gathered for the all-day event featuring numerous well-known Russian rock bands.
"If the explosions had occurred on the field itself, the consequences would have been far more serious," Gryzlov added.
|Russian police officer looks at the|
body of one of the suspected
Chechen fighters have in the past employed suicide bombers and have attacked Moscow events, including a theatre show last year.
Russia media reported Moscow hospitals preparing beds for an influx of injured.
Despite the presence of thousands of Russian troops, Chechen fighters have vowed to continue to their campaign in the mountainous region to oust the military
But many rebels reject the use of suicide bombers.
Last October's attack on the Moscow musical theatre turned into a siege at the end of which 129 hostages and 41 guerrillas died, all but two of the captives, from the effects of a gas used by Russian special forces to disable the hostage-takers.
The small, mainly Muslim region on Russia's southern Caucasus fringe secured de facto independence in 1996 after Russia's first, botched military intervention. But troops were dispatched back to the region in 1999.