Moscow claimed on Wednesday to have foiled a Ukrainian attempt to assassinate Russian President Vladimir Putin.
Ukrainian President Volodymyr Zelenskyy said his country did not attack Moscow or Mr Putin, telling reporters in Helsinki: “We’ll leave it to tribunal.”
Mr Zelenskyy said the Kremlin was probably trying to distract Russians from its failures on the battlefield.
“We fight on our own territory, where we are defending our own villages and cities," he said. "We don’t have enough weapons for this.”
The US said it could not verify the claim, which comes in the lead-up to a military parade in Moscow on May 9.
Drone flights were banned in Moscow as Russia warned it "reserves the right to take retaliatory measures".
Moscow said the drones had been "put out of action" by Russian defences using "radar warfare systems". It said Mr Putin was unhurt.
Footage surfaced purporting to show a late-night flash of light at the Kremlin, but its origin and authenticity were not clear.
Senior Ukrainian officials denied involvement and suggested Russia was looking for a pretext for further attacks.
"Ukraine wages an exclusively defensive war and does not attack targets on the territory of the Russian Federation," said presidential aide Mykhailo Podolyak.
"As you know, drones can be bought at any military store."
US Secretary of State Antony Blinken said he had seen the reports but could not "in any way validate them".
"I would take anything coming out of the Kremlin with a very large shaker of salt. We’ll see what the facts are," Mr Blinken said.
Former Russian president Dmitry Medvedev called for the "physical elimination" of Mr Zelenskyy after the claimed drone attack.
"After today's terrorist attack, there are no options left aside from the physical elimination of Zelenskyy and his cabal," said Mr Medvedev, who has been increasingly hawkish since Moscow's Ukraine offensive.
The claim follows mysterious explosions and acts of sabotage behind Russian lines, with Ukraine generally remaining silent about any involvement.
Kremlin spokesman Dmitry Peskov said Mr Putin would still take part in the planned parade on May 9, which commemorates the Soviet victory in the Second World War.
The remnants of the downed drones fell inside the Kremlin but did not injure anyone, the Kremlin said.
“We regard these actions as a planned terrorist act and an attempt on the President's life, carried out on the eve of Victory Day, the May 9 parade, at which the presence of foreign guests is also planned," it said.
“The Russian side reserves the right to take retaliatory measures where and when it sees fit.”
Shortly before the Kremlin statement was released, Moscow city authorities issued an order banning the use of drones in the capital.
Mayor Sergei Sobyanin said drone flights would be prohibited unless a special permit had been obtained from “government authorities”.
The ban was meant to prevent unauthorised drone flights that could “obstruct the work of law enforcement”, Mr Sobyanin said.
The mysterious video was posted in the early hours of Wednesday on a group for residents of a neighbourhood that faces the Kremlin across the Moskva River, and picked up by Russian media, including the Telegram channel of the military news outlet Zvezda.
The news about the alleged drone attack came as Ukraine prepared for a new offensive against Russian troops, which it has been planning for months.
In possible signs that preparations are being increased, the front-line city of Kherson in southern Ukraine announced a long curfew for residents, as sabotage acts behind Russian lines intensified.
Kherson, which was retaken by Ukrainian troops in November, will be under curfew from Friday evening until Monday morning.
Regional officials said this was “for law enforcement officers to do their job”, but similar long curfews have also been used in the past for troop and arms movements.
“During these 58 hours, it is forbidden to move on the streets of the city. The city will also be closed for entry and exit,” the head of Kherson's regional military administration, Oleksandr Prokudin, said on Telegram.
He advised residents to stock up on food and medicine, and said people could go for short walks near their houses or visit shops but should carry identity documents with them at all times.
The curfew announcement came as officials said three people were killed and five injured in a Russian strike on Kherson's only working hypermarket on Wednesday.
Kherson was captured by Russian troops last year in the first days of the invasion and remained under Russian occupation until November.
After a sustained campaign of sabotage attacks behind Russian lines, Russian forces withdrew from the city.
They crossed to the eastern side of the Dnipro River which now forms part of the front line in southern Ukraine.
The curfew announcement came as officials in Russia said they were dealing with a major fire at a fuel depot close to the bridge to Russian-annexed Crimea, the second such incident in just a few days.
A source in the emergency services was quoted by Tass news agency as saying that the fire had been caused by a drone.
An explosion also caused a freight train to derail in a southern Russian region bordering Ukraine on Tuesday, also the second such incident in two days.
Ukraine says it has been preparing for months for a counteroffensive aimed at repelling Russian forces from the territory they hold in the east and south.
Meanwhile, Mr Zelenskyy was on a surprise visit to Finland, Nato's newest member, to take part in a summit with the leaders of the five Nordic nations, which have been key providers of military aid.
“In order to be in Nato and support alliances to gain support, fundamental diplomatic work must be done. Ukraine is doing it today,” Daria Zarivna, Ukraine's presidential communications adviser, wrote on Telegram.
