Russia has warned of “irreversible consequences” after a man was allegedly killed on its side of the border by a shell fired from Ukraine.
A Foreign Ministry statement blamed Ukrainian government forces for the “provocation”.
Ukrainian Security Council spokesman Andriy Lysenko said its forces were not firing on Russian territory.
A rebel attack on government troops on Friday which left 19 soldiers dead has led to a spate of further clashes.
At least four people died the following night when a suburb of the rebel-held Ukrainian city of Donetsk, Marinka, was badly damaged by rockets.
The pro-Russian separatist rebel leadership and the government blamed each other for that attack.
At least 12 civilians and three service personnel are reported to have been killed in other incidents since.
The rebels, who declared independence in Donetsk and Luhansk regions in April, retreated towards the city of Donetsk last week after a government siege of their symbolic stronghold, Sloviansk.
More than 1,000 civilians and combatants are believed to have died in the fighting since April.
The latest alleged incident happened when a shell hit the courtyard of a residential building in a small Russian border town, also called Donetsk, early on Sunday.
A man was killed and at least one person seriously injured.
This is believed to be the first time Russia has reported a fatality on its side of the border.
Russian Deputy Foreign Minister Grigory Karasin described the reported incident as an “extremely dangerous escalation for Russian citizens on Russian territory”.
“The conversation with the Ukrainian side on this issue will be serious and tough.” he told Russian radio.
A foreign ministry statement warned of “irreversible consequences, the responsibility for which lies on the Ukrainian side”.
Mr Lysenko described the accusations as “total nonsense”.
“The forces of the anti-terrorist operation do not fire on the territory of a neighbouring country and they do not fire on residential areas,” he said.
“We have many examples of terrorists carrying out provocative shooting, including into Russian territory, and then accusing Ukrainian forces of it.”
The row came as Ukrainian President Petro Poroshenko announced that he would not be attending the football World Cup final in Brazil.
He had been expected to meet his Russian counterpart Vladimir Putin there to discuss the crisis.