Russia has threatened Ukraine with "irreversible consequences" after a man in Russia was killed from a shell fired allegedly from Ukraine.
President Vladimir Putin expressed "grave concern" over the incident on July 13, according to a Kremlin spokesman.
Kyiv denied its forces had fired across the border, calling such charges "total nonsense."
Ukrainian officials suggested pro-Russian separatists could have been responsible, hoping to provoke Moscow to intervene on their side.
The Ukrainian Foreign Ministry urged Russian authorities to carry out "an objective and impartial" probe of what it called "a tragic incident," and offered to help.
The rebels denied blame.
Russia's Investigative Committee said a shell had landed in the yard of a house in a small town on the Russian side of the frontier, killing a man and wounding a woman.
The town is called Donetsk, bearing the same name of what the rebels have declared capital of an independent Donetsk "people's republic."
Many rebels have regrouped in the city of Donetsk after Ukrainian forces retook several towns and villages in the region of Donetsk and neighboring Luhansk.
Kyiv Urges EU Action
Meanwhile, Ukraine's President Petro Poroshenko has accused Russian forces of crossing the border and attacking Ukrainian servicemen.
His comments came in a telephone call on July 13 with the European Council President Herman van Rompuy.
According to his website, Poroshenko called on the European Union to condemn "the illegal crossing of the Russian-Ukrainian border with heavy military equipment and an attack by Russian soldiers on the positions of Ukrainian servicemen."
Poroshenko's remarks came after a report by Ukraine's "antiterrorist operation" claimed that a convoy of some 100 separatist armored vehicles and trucks had crossed into Ukraine carrying rebels from Russia.
Ukraine's military said the column had been bombarded, although details are unclear. It also said seven of its troops had been killed in attacks.
Putin and German Chancellor Angela Merkel agreed the situation in east Ukraine was "deteriorating."
Meeting ahead of the World Cup final in Brazil, Merkel and Putin called for peace talks between Ukraine and the rebels to be held as soon as possible.
Ukrainian defense officials said on July 13 that the air force had carried out 16 sorties and five air strikes on rebel positions over the previous day.
Rebels controlling Luhansk said Ukrainian forces were closing in on the city with tanks and warplanes.
Eastern Ukraine has witnessed an increase in fighting since the killing of 19 Ukrainian soldiers in a rocket attack by pro-Russian separatists on July 11.