Russia has vowed to step up attacks on Kyiv in response to any Ukrainian attacks on Russian territory.
Kyiv was hit on Friday by some of the most powerful explosions heard since Russian forces withdrew from the area weeks ago.
Moscow said it had struck a plant that made and repaired Ukrainian missiles, including anti-ship missiles.
It claimed the strike was in retaliation for a Ukrainian helicopter attack on a Russian village near the border, which Kyiv denies.
In a statement, the Russian Defence Ministry said: “The number and scale of missile strikes on targets in Kyiv will increase in response to any terrorist attacks or acts of sabotage on Russian territory committed by the Kyiv nationalist regime”.
Kirill Kyrylo (38) a worker at a car repair shop, said he had seen three blasts hit an industrial building across the street, causing a blaze that was later put out by firefighters.
“The building was on fire and I had to hide behind my car," he said, pointing out the shattered glass of the repair shop and bits of metal that had flown over from the burning building.
Russia’s defence ministry also claimed it had captured the Ilyich steel works in Mariupol, the eastern port which has been under heavy bombardment. This has not been confirmed.
The statement comes after the sinking of Russia’s flagship warship, the Moskva, which is widely thought of as a humiliating set-back for Russia’s Black Sea fleet.
Ukraine said it had hit the ship with missiles fired from the coast, but Moscow claims it sank while being towed to port in stormy seas after a fire caused an explosion of ammunition.
The Moskva was by far Russia’s largest vessel in the Black Sea fleet, equipped with guided missiles to shoot down planes and attack the shore, and radar to provide air defence cover for the fleet.
Hours before it was allegedly hit, Ukraine released a postage stamp with a picture of a soldier making an obscene gesture towards the ship.
The stamp commemorated the invasion of Snake Island, when the Moskva’s crew ordered Ukrainian defenders to surrender, only to be told, “Russian warship, go f*** yourself.
Ukraine’s president Volodymyr Zelensky paid homage to "those who showed that Russian ships can go -- only down to the bottom".
“If reports of Moskva’s sinking prove true it will be emblematic of Russia’s overall military effort thus far," tweeted Michael Kofman, an expert on Russia’s military, who called it a "major loss for the Russian navy”.
No warship of such size has been sunk during conflict since Argentina’s General Belgrano, which was sunk by the British in the Falklands war in 1982.
Russia has warned the United States that there will be "unpredictable consequences" if Washington keeps arming Ukraine, The Washington Post reported on Friday.
"We call on the United States and its allies to stop the irresponsible militarisation of Ukraine, which implies unpredictable consequences for regional and international security," the Post quoted Russia saying in a diplomatic note to the United States.
The latest comes as Russia's communications watchdog has blocked access to the Russian language website of The Moscow Times, a newspaper that has covered Russia for three decades since the collapse of the Soviet Union.
The Moscow Times said Russian internet providers had already started to block its Russian-language site. It published a notice from Russia's communications watchdog which said its site was now blocked.
Kyiv has gradually displayed some signs of pre-war life after Russian troops failed to capture the city and retreated to focus on a concentrated assault in eastern Ukraine, leaving evidence of possible war crimes in their wake. A renewed bombardment could return the capital's residents to sheltering in subway stations and the steady wail of air raid sirens.
Ukrainian officials have not confirmed striking targets in Russia, and the reports by Russian authorities could not be independently verified. However, Ukrainian officials claimed their forces struck a key Russian warship with missiles on Thursday. If true, the claim would represent an important victory.
In his nightly address on Thursday, Ukrainian President Volodymyr Zelensky said the people of his country should be proud of having survived 50 days under attack when the Russian invaders "gave us a maximum of five".
Mr Zelensky did not mention the Moskva by name, but while listing the ways Ukraine has defended against the onslaught, mentioned "those who showed that Russian warships can sail away, even if it's to the bottom" of the sea. It was his only reference to the Moskva.
News about the flagship overshadowed Russian claims of advances in the southern port city of Mariupol, where Moscow's forces have been battling the Ukrainians since the early days of the invasion in some of the heaviest fighting of the war - at a horrific cost to civilians.
Dwindling numbers of Ukrainian defenders in Mariupol are holding out against a siege that has trapped well over 100,000 civilians in desperate need of food, water and heating. David Beasley, executive director of the UN World Food Programme, said people were being "starved to death" in the besieged city.
Mariupol's mayor said this week that more than 10,000 civilians had died and the death toll could surpass 20,000. Other Ukrainian officials have said they expect to find evidence of atrocities committed against civilians like the ones discovered in Bucha and other towns outside Kyiv once the Russians withdrew.
The Mariupol City Council said on Friday that locals reported seeing Russian troops digging up bodies that were buried in residential courtyards and not allowing any new burials "of people killed by them".
"Why the exhumation is being carried out and where the bodies will be taken is unknown," the council said in a statement posted on the Telegram messaging app.
Mariupol's capture is critical for Russia because it would allow its forces in the south, which came up through the annexed Crimean Peninsula, to fully link up with troops in the Donbas region, Ukraine's eastern industrial heartland and the target of the looming offensive.
Moscow-backed separatists have fought Ukrainian forces in the Donbas since 2014, the same year Russia seized Crimea from Ukraine. Russia has recognised the independence of two rebel-held areas of the region.
Although it is not certain when Russia will launch the full-scale campaign, a regional Ukrainian official said Friday that seven people died and 27 were injured after Russian forces opened fire on buses carrying civilians in the village of Borovaya, near the north-eastern city of Kharkiv.
Ukrainian law enforcement agencies are working to establish the circumstances of the attack, said Dmytro Chubenko, a spokesman for the regional prosecutor's office.
Mr Chubenko said that Ukrainian authorities had opened criminal proceedings in connection with a suspected "violation of the laws and customs of war, combined with premeditated murder". The claims of an attack on civilian buses could not be independently verified.
The Russian Defence Ministry said on Friday that Russian strikes in the Kharkiv region "liquidated a squad of mercenaries from a Polish private military company" of up to 30 people. The claims could not be independently verified.
On Thursday, the Defence Ministry explained the damage to Russia's Black Sea flagship by a fire had caused ammunition stowed on board to detonate. In addition to the cruise missiles, the warship also had air-defence missiles and other guns.
The ministry did not say what might have caused the blaze but reported that the "main missile weapons" were not damaged and the crew, which usually numbers about 500, abandoned the vessel. It was not clear if there were any casualties.
Maksym Marchenko, the governor of Ukraine's Black Sea region of Odesa, said Ukrainian forces struck the Moskva with two Neptune missiles and caused "serious damage". The Neptune is an anti-ship missile that was recently developed by Ukraine based on an earlier Soviet design.
The missile's launchers are mounted on trucks stationed near the coast, and, according to the Washington-based Centre for Strategic and International Studies, can hit targets up to 175 miles away. That would have put the Moskva within range, based on where the ship was when the fire began.
British defence officials said the Moskva's loss would probably force Moscow to change how its naval forces operate in the Black Sea. In a social media post, the Ministry of Defence said the ship, which returned to operational service last year after a major refit, "served a key role as both a command vessel and air defence node".
Russia invaded Ukraine on Febraury 24 and has suffered thousands of military casualties. The conflict has killed untold numbers of Ukrainian civili