Russia has promised to respond with "irreversible consequences" to a "dangerous escalation" of violence near its border, after a Russian man was killed and two women injured by shells fired across the Ukraine border.

Alexander Titov, a spokesman for the regional government in Rostov, told the Russian news agency Itar Tass that a shell damaged two homes at about 5.20am GMT in Donetsk, a town of the same name as the city in eastern Ukraine.

The Russian town of Donetsk is near the border with Ukraine's Luhansk region, where Kiev-backed troops and pro-Russian separatists are fighting for the control of border checkpoints.

Grigory Karasin, Russia's deputy foreign minister, said the incident represented a "dangerous escalation for our citizens" and promised it "will not be left without a response", in televised remarks.

His ministry said the bombing was "an aggressive act by the Ukrainian side against sovereign Russian territory and the citizens of the Russian Federation".

Al Jazeera's Peter Sharp, reporting from Moscow on Sunday, said it was the first time a Russian citizen had been killed during the three-month-old conflict.

"What they [the Russians] are saying is this is an incident that would not be allowed to pass," he said.

The Russian Foreign Ministry on Saturday warned Ukraine over what it says are continued attacks on its territory during the conflict, saying it "has the right to take measures to protect its territory and ensure the security of Russian citizens".

Ukraine has denied firing on Russian territory, and suggested the attack could have been the work of pro-Russian rebels trying to provoke Moscow to intervene on their behalf. The rebels denied they were responsible.

Andriy Lysenko, a spokesman for Ukraine's security council, was quoted by Interfax news agency 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, and condemned the shelling as a "provocation".