Ukrainian Presidential adviser Mykhailo Podolyak responded, saying Kyiv had nothing to do with any drone attack on the Kremlin, and that such actions achieved nothing for Kyiv on the battlefield and would only provoke Russia to take more radical action.
He said in comments sent to Reuters that such allegations, and Russia's arrest of alleged Ukrainian saboteurs in Crimea, could indicate Moscow was preparing for a large-scale "terrorist" attack against Ukraine in coming days.
The alleged thwarted operation comes on the heels of a series of incidents - including trains sabotage - ahead of the popular WWII victory celebrations.
"Today at night, the Kyiv regime attempted to strike the Kremlin residence of the President of the Russian Federation with unmanned aerial vehicles," the Kremlin said.
"Two unmanned aerial vehicles were aimed at the Kremlin," it said.
"We regard these actions as a planned terrorist act and an attempt on the life of the President of the Russian Federation."
Moscow said Putin was not wounded and its forces downed the drone without any casualties.
It said that debris from the drone "fell on the territory of the Kremlin."
Authorities have tried to reassure Russians that the conflict is distant and does not pose a threat to Russian territory.
A recent series of apparent sabotage attacks have served as a reminder that Russia is exposed to enemy blows.
They hit as Moscow is gearing up for May 9 celebrations when Russia marks the Soviet victory over the Nazis in what has become a central event for Putin's rule.
Kremlin spokesman Dmitry Peskov said the parade in Moscow was going ahead as expected with "no changes to the plans," according to news agencies.
Also on Wednesday, Moscow's mayor Sergei Sobyanin announced a ban on unauthorised drone flights over the Russian capital.