Russia accused the West of enabling Ukraine to carry out the drone attacks.
Moscow said Ukrainian drone attacks on Russian territory would "not be possible" without US and NATO help, ratcheting up its rhetoric after reporting it had downed five drones near the capital on Tuesday.
Ukraine meanwhile said 43 people, including 12 children, were injured in a Russian strike on the town of Pervomaisky in the eastern Kharkiv region.
Moscow accused the West of enabling Ukraine to carry out the drone attacks, after earlier condemning what it called a "terrorist act".
"These attacks would not be possible without the help provided to the Kyiv regime by the US and its NATO allies," the Russian foreign ministry said, claiming the West was "training drone operators and providing the necessary intelligence to commit such crimes."
It marks the latest in a series of recent drone attacks -- including on the Kremlin and Russian towns near the border with Ukraine -- that Moscow has blamed on Kyiv.
The Russian military said it had downed all five drones and that there was no damage or casualties from the early-morning attacks.
Emergency services cited by the state-run RIA Novosti news agency said one of the drones was "neutralised" at Kubinka, about 40 kilometres (25 miles) from Vnukovo international airport, where air traffic was briefly disrupted.
In early May, two drones were shot down above the Kremlin, and later the same month drones hit Moscow high-rises.
- Burning, overturned cars -
Kyiv said early Tuesday that Russia had launched 22 Iranian "Shahed" attack drones and three missiles at the Sumy, Donetsk and Zaporizhzhia regions.
Its forces had "destroyed" 16 of the drones, it said.
The strike in the eastern Kharkiv region bordering Russia hit a parking lot outside a residential building in Pervomaisky, a town of around 28,000 people.
The head of Kyiv's presidential office Andriy Yermak distributed images of burned and destroyed cars.
The governor of the Kharkiv region, Oleg Synegubov, posted a video from the scene, showing smoke rising from burnt cars near a Soviet-era housing block.
He said 43 people were injured, among them 12 children.
Authorities also announced that Russian shelling on a residential area in the southern frontline city of Kherson had killed two people.
- Zaporizhzhia accusations -
Late on Tuesday Ukraine accused Russia of planning a "provocation" at the Moscow-controlled Zaporizhzhia nuclear power plant, while Russia claimed Kyiv was planning to attack the facility.
The two sides have regularly accused each other of putting the plant's safety at risk since the start of the conflict.
Kyiv claimed "objects similar to explosive devices were placed on the outer roof of the third and fourth reactors" at the site, which is Europe's largest.
"Their detonation should not damage power units, but may create a picture of shelling from the Ukrainian side," it said, alleging that Moscow would "misinform on this".
In Moscow, an advisor to Russia's Rosatom nuclear agency, Renat Karchaa, told state television: "On July 5, literally at night, in the dark, the Ukrainian army will try to attack the Zaporizhzhia nuclear power plant".
He claimed Ukraine planned to use "high-precision, long-range weapons" as well as drones.
- Journalist attacked -
In Chechnya, an award-winning Russian investigative journalist was beaten by armed assailants and taken to hospital, her newspaper and a rights group said.
The attack happened early on Tuesday as well-known journalist Elena Milashina and Alexander Nemov, a lawyer, were travelling from the airport.
Her newspaper, Novaya Gazeta, published a video of Milashina in hospital with her head shaven and covered in a green-coloured dye -- used to target Kremlin critics -- and her hands bandaged.
She said the attack, which included having a gun held to her head, was linked to her "professional activity in Chechnya."
Milashina has for years covered rights abuses in the Caucasus republic ruled by former warlord Ramzan Kadyrov.
She came to Grozny to attend the sentencing of Zarema Musayeva, whose husband and sons have fallen foul of the Kadyrov regime, but did not make it there.
"It's a sensitive case," she said, calling Musayeva a "hostage."
Musayeva was later handed five-and-a-half years on fraud charges widely seen as political revenge against her family.
In Kyiv, around 200 people attended a ceremony on Tuesday in St Michael's cathedral for the Ukrainian writer Victoria Amelina, who died of her wounds in a Russian strike on a restaurant in eastern Ukraine.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)