Russian authorities accused Ukraine of trying to kill investigators who were checking reports of cross-border shooting by firing a volley of mortar rounds over the frontier into Russia on Friday.
A Russian security official said up to 40 mortar bombs fired by Ukrainian forces fell in the Russian province of Rostov near the border where Ukrainian government forces are fighting pro-Russian separatists.
There were no reports of injuries.
Russia's Investigative Committee said: "Those who shot from Ukraine carried out the shooting purposefully with an intent to kill Russian law enforcement officials."
"It was only the poor preparation of the Ukrainian military and the timely evacuation of law enforcement officers under the cover of armoured transport vehicles that did not allow the shooters to realise their intention," it said in a statement.
Accusations by pro-European authorities in Ukraine, its western backers and Russia over cross-border fire have boosted tensions in the worst crisis between Russia and the West since the end of the Cold War.
Russia's foreign ministry also criticised Washington one day after it said Russia was firing artillery across the border into Ukraine to target Ukrainian military positions.
"We deny the unfounded public insinuations that State Department spokeswoman [Marie] Harf repeats day after day," the ministry said in a statement.
"In journalistic briefings in previous days she has produced anti-Russian clichés that Washington stubbornly tries to impose on international opinion," the statement said.
The Investigative Committee, which answers only to President Vladimir Putin, said its officers were indentifiable as law enforcement officials and were in Rostov province's Kuybyshevsky region to look into previous accounts of cross-border shelling.
The committee has thrust itself to the fore of the crisis between Russia and Ukraine, accusing Ukrainian Interior Minister Arsen Avakov and Ihor Kolomoisky, a provincial governor, of criminal acts in the government's military push against rebels.
Vasily Malayev, a regional representative of Russia's Federal Security Service branch devoted to border security, was quoted by Russian news agency Interfax as saying that 30 mortar rounds had landed in a village in the region.
He earlier told state RIA Novosti news agency that around 40 shells had come across the border.
Ukraine says missiles shot from Russia may have downed two of its fighter jets this week. Moscow denies the accusation.
Russia's Chief of General Staff was quoted as saying by Interfax that it had proof that Ukraine had used phosphorus bombs that can kill through burns or smoke inhalation.
Earlier allegations of the use of the weapon were never proved and Kiev quickly denied this accusation.
"It's complete nonsense. We don't use phosphorus bombs. We simply don't have them. We use flares, but they have no relation to phosphorus bombs," Kiev's military spokesman, Vladislav Seleznyov, said.