Footage showed a flying object exploding in flames overnight above the fortress in central Moscow where the president has his office and an apartment.
Putin, 70, was not inside at the time and was not injured, the Kremlin said.
But the Kremlin blasted the alleged strike as a “planned terrorist action” – and said it reserves the right to retaliate.
And the Speaker of the Russian parliament Vyacheslav Volodin – an intimate Putin ally – appeared to demand a nuclear strike on Ukraine.
He raged: “An attack on the president is an attack on Russia.
“There can be no negotiations. We will demand the use of weapons that are capable of stopping and destroying the Kyiv terrorist regime.”
Moscow’s nuclear doctrine clearly states their forces can use nuclear weapons when the country’s “very existence” is at risk.
Russian authorities claim they downed two unmanned aerial vehicles that were aimed at the presidential complex – where Putin is known to increasingly live during the war.
Extraordinary footage appeared to show the moment a drone exploded over the Senate Palace, with flames and smoke seen coming from the 18th century dome at 2.27am.
Grandstands set up for the Victory Day parade on May 9 can be seen in Red Square below, in front of the fortress walls.
A second blast was seen over the rooftops at 2.43am.
Residents of nearby Stalinist House on the river embankment said they “saw sparks in the sky and people with flashlights near the Kremlin wall after the thunderclaps”.
The Kremlin said two drones had been used in the alleged attack, but were disabled by Russian electronic defences.
But today, as workmen examined the roof for damage, there was incredulity at how the drones could have got past Moscow’s ring of steel air defences.
One Russian Telegram channel cited sources suggesting the whole thing could have been staged.
It claimed: “Shooting down such objects above the [Kremlin] towers is prohibited by protocol, so reports of downed UAVs are nonsense.
“Or they exploded on their own.
“Or all this was an exercise, a performance, that they decided to pass off as a real attack.”
Adding to the mystery, eagle-eyed viewers spotted that at least two people were standing on the dome at the time of the explosion.
The twin blasts came after a wave of kamikaze drone strikes against Russian targets in Crimea and elsewhere.
Ukraine has not acknowledged its suspected role in those attacks, and has denied drone hits on the Russian mainland.
And today Zelensky’s press secretary distanced Kyiv from the apparent Moscow attack.
The spokesman said: “We have no information about the so-called night attacks on the Kremlin.
“But, as President Zelensky has repeatedly stated, Ukraine directs all available forces and means to liberate its own territories, and not to attack others.”
Key Zelensky adviser Mykhailo Podolyak said the attack may have come from “guerrilla activities of local resistance forces” in Russia.
He said: “As you know, drones can be bought at any military store…
“The loss of power control over the country by Putin’s clan is obvious.
“But on the other hand, Russia has repeatedly talked about its total control over the air.
“In a word, something is happening in Russia, but definitely without Ukraine’s drones over the Kremlin.”
‘Pretext for war’
Officials said Putin spent last night at his official residence at Novo-Ogarevo, outside the capital, and his schedule would not change.
He was later pictured in a meeting with Nizhny Novgorod region governor Gleb Nikitin.
But such photo-ops are often “canned” in advance, making it impossible to know if the meeting took place today.
Putin allies reacted to the alleged attack with alarming calls for revenge.
Former Russian president Dmitry Medvedev – now a top Putin security official – called for the “elimination” of Zelensky.
In a chilling statement, he said: “After today’s terrorist attack, there are no options left except for the physical elimination of Zelensky and his cabal.
“It is not even needed to sign an act of unconditional surrender.”
Pro-Putin Just Russia party leader Sergey Mironov added: “This is the very real casus belli – a pretext for war.”
He urged the “liquidation of Ukraine’s terrorist top brass. We have something to hit their bunkers with.”
Senior politician Alexei Zhuravlev urged: “It is necessary to target the centre of Kyiv.
“Destroy the president’s office, destroy to the ground the [Ukrainian parliament], the general staff, and the buildings housing the Ukrainian special services.”
MP Mikhail Sheremet said: “It’s time to launch a missile strike on Zelensky’s residence in Kyiv.”
Russia has already failed to assassinate Zelensky more than a dozen times, it is claimed.
It comes just days after it was claimed Kyiv tried to kill Putin using a drone packed with explosives.
The wreckage of a Ukrainian-made drone was discovered just a few miles from Moscow and it’s believed it either overflew or was circling the Russian capital.
The alleged attacks come after paranoid Putin reportedly ramped up air defence systems around Moscow.
Pantsir-S1 and S-400 defence systems have been positioned on rooftops across the capital, which are designed to intercept missiles and aircraft.
Meanwhile, Ukraine has been suspected of being behind a wave of kamikaze drone strikes on Russian targets including an oil depot and military airfield.
An attack on a headquarters of the FSB spy service and a train are also believed to be the work of Kyiv’s forces.
The first attack sent smoke thousands of feet into the air near to Putin’s prized bridge linking Russia to Crimea, which he annexed in 2014.
The attack is the latest in a rising tide of apparent strikes by Ukraine on Russian territory in the war between the two countries.
Kyiv is suspected of being behind a mass drone attack on a Russian military air base in the Bryansk region.
Two drones were shot down using small arms but two exploded on the airfield, with one damaging a giant ‘Ruslan’ An-124 transport plane and putting it out of service, according to Russian media reports.
In another attack, a blast rocked a secret training base of the FSB security service near Simferopol, the capital of Crimea.
The site is reportedly used by Russian border guards, part of the FSB, and crucial to Putin’s illegal control of a region.
Meanwhile, a freight train made up of 20 oil tanker carriages derailed, also in the Bryansk region, the second track explosion in two ways.
The attack comes just days after Ukrainian forces were believed to have hit an oil depot in Crimea itself.
Ukrainian drones have already crashed near Moscow while Kyiv has been suspected of behind sabotage attacks carried out near the city.
Kyiv plotted an audacious attack on Moscow to mark the first anniversary of Russia’s invasion, leaked spy documents have revealed.
The mass strikes were ultimately called off after the United States intervened and warned Kyiv its plan could lead to a nuclear war.