Russia's foreign ministry said that a Ukrainian shell hit a Russian border town, killing one person and seriously injuring two others.
But Ukraine denied firing a shell into Russian territory.
A statement from Russia's foreign ministry labelled the incident a "provocation," and warned of the possibility of "irreversible consequences, the responsibility for which lies on the Ukrainian side".
Russia said the shell hit the courtyard of a residential building in the Russian town of Donetsk - near the Ukrainian city of the same name that has become a rebel stronghold. Ukraine's restless east has been mired in a pro-Russian separatist insurgency against the Kiev government.
Ukrainian officials denied that any Ukrainian shells had fallen on Russian territory. Andriy Lysenko, a spokesman for Ukraine's National Security and Defence Council, was quoted by Interfax Ukraine as saying that Ukrainian forces "do not fire on the territory of a neighbouring country. They do not fire on residential areas."
He placed blame for the attack on the rebels themselves.
Russia has made repeated claims that settlements along its porous border with Ukraine - which the West and Kiev say is a key supply route for the rebels - have been hit by Ukrainian fire, but no deaths have been previously reported.
The claims come as President Vladimir Putin, whose nation will host the 2018 World Cup, is attending the final in Rio de Janeiro to take part in a handover ceremony with Brazilian president Dilma Rousseff and Fifa president Sepp Blatter.
Brazilian officials said that both Mr Putin and his Ukrainian counterpart, Petro Poroshenko, would attend the match. But Mr Poroshenko announced today that he would not be going.
Talks between Russia and Ukraine over a ceasfire between the rebels and Kiev's troops have stalled in recent weeks, as Ukrainian troops have succeeded in pushing insurgents out of key towns in the east.
Ukraine's Donetsk, where rebels have gathered to regroup after a major Ukrainian offensive last week, was quiet today. But some 150 people from the settlement of Marynka, on the outskirts of the city, were moving into dormitories at a local university after their homes were bombarded during the night.
"We were brought here this morning," said Svetlana Panteleyeva, who was with her grandson. "We were bombed so terribly.... They blew up our houses."
Artillery fire in Marynka late on Friday left at least four people dead, but the number of casualties in the latest bombing was unclear.
Ukrainian defence officials said that the air force had performed 16 sorties and carried out five air strikes on rebel positions over the previous day.
Interfax-Ukraine cited Mr Lysenko as saying that several dozen rebels had been killed and rocket launchers and armoured vehicles destroyed in the attacks. He also said that seven servicemen had been killed and 30 wounded in the past day.
Following the loss of at least 19 soldiers in a rocket attack on Friday morning by the pro-Russian militia, Ukrainian officials have claimed to have killed large numbers of rebel combatants, although there has been no independent verification. Late on Friday, Defence Ministry spokesman Vladislav Seleznev said on his Facebook account that 1,000 rebels had been killed in two separate air strikes.
Mr Poroshenko vowed last week to respond with firmness to attacks by the pro-Russian insurgency.
"For every life of our soldiers, the militants will pay with tens and hundreds of their own," Mr Poroshenko warned. "Not one terrorist will evade responsibility. Everybody will get what is coming to them."