Ukraine used two drones to attack the Kremlin - in the heart of Moscow - overnight.
It appears that Russian forces used radar equipment to disable the two planes. The statement added that there were no injuries and the president was not harmed.
But the Kremlin called it an "assassination attempt" targeting Vladimir Putin.
A number of videos appeared. It appears to show at least one drone flying towards the Kremlin, followed by an explosion. Another shows smoke rising from a building in the Kremlin, and a fire.
But if what the Kremlin says is true, and this was a genuine attempt on the president's life, it would be a very embarrassing incident for the Kremlin.
By all accounts, Putin appears to be one of the most closely guarded leaders in the world. At its events in Moscow attended by BBC journalists, very tight security was imposed, including extensive checks and long convoys of vehicles, with airspace closed and traffic halted.
And questions will now arise about how well the Russian leader is protected — and about the effectiveness of Russia's air defenses.
In recent months, anti-aircraft systems have been seen on rooftops in Moscow near key buildings, including the Defense Ministry.
It was put there precisely for this reason — because the Kremlin is concerned that Ukraine, or those sympathetic to Ukraine, might try to carry out air strikes on high-value targets.
If reports of the latest incident are true, those measures have failed.
This attack is the latest in a series of attacks and explosions that have hit Russian territory in recent weeks and months.
The past few days have seen a sharp rise in such incidents.