Russian President Vladimir Putin's spokesperson Dmitry Peskov says the Kremlin no longer has any influence over rebels in the east of Ukraine.
"From now on Russia essentially has lost its influence over these people because it will be impossible to convince them to lay down arms when there's a direct threat to their lives," he said.
Mr Peskov added that "speaking about elections is absurd to say the least."
Asked how Russia would respond to the escalating crisis, Dmitry Peskov told Russian news agencies: "I cannot answer this question, it's an absolutely new element for us."
But he also said that both the Kiev authorities and their backers in the West were directly responsible for bloodshed in the Ukrainian city of Odessa.
"Kiev and its Western sponsors are practically provoking the bloodshed and bear direct responsibility for it," RIA Novosti quoted Mr Peskov as telling reporters.
Other agencies also quoted Mr Peskov as saying that Russia had lost influence over the so-called self-defence forces in the south-east Ukraine, and could not resolve the situation by itself.
His reported comments came after Ukraine said it was continuing military operations against pro-Russian separatists in the industrial east of the country, with a dawn strike near the town of Kramatorsk.
The Interior Minister Arsen Avakov said Ukrainian forces had seized control of a television tower in Kramatorsk, near the rebel stronghold of Sloviansk where there was heavy fighting overnight.
At least 38 people died earlier on Saturday, in a fire that broke out after clashes between pro-Russian militants and government supporters in the south-western city of Odessa.
Moscow's ambassador to the United Nations warned of what he called "catastrophic consequences" if Kiev's military operation in eastern Ukraine continued.
But, the United States told the United Nations Security Council that Ukraine's reaction had been proportionate and reasonable".
The US State Department said the fire pointed to a need for an "immediate de-escalation" of tensions.
And Ukraine said it won't stop its military operations.
Violence also spread across the country, with reports of renewed fighting in Sloviansk leading to the deaths of two more Ukrainian soldiers.
That means at least nine people were killed in violence in that flashpoint eastern town in one day.
It's unclear what caused the fire at Odessa's trade union building, but reports said both sides had been throwing petrol bombs.
More than 130 people have been detained that southern port city of Odessa after the fire and the preceding street fighting involving pro-Russian and groups supporting the government in Kiev.
The local police chief sais those detained could face charges ranging from participating in riots to premeditated murder for overnight street battles.
Officials said most of those killed either choked on smoke or died after jumping out of the building's windows.
The police quickly lost control as hundreds of men including soccer fans staged running battles across the city.
On Monday, Kharkiv mayor Hennadiy Kernes was shot and critically wounded.
More sanctions mooted
The UN Security Council met on Friday for an emergency session at Russia's request and President Obama met Chancellor Angela Merkel of Germany at the White House.
Afterwards, Mrs Merkel said Europe is prepared to support sanctions targetting entire sectors of the Russian economy.
Mr Obama said the Russian account of events in eastern Ukraine that there was a spontaneous uprising by pro-Russian activists was belied by the use on Friday of surface-to-air missiles that brought down two military helicopters.
"It is obvious to the world that these Russian-backed groups are not peaceful protesters. They are heavily armed,'' he said.
Eastern Ukraine has a large Russian-speaking population. The Crimean peninsula was annexed by Russia after a referendum on 16 March.
Odessa is a city of one million people, on the Black Sea coast, close to the border with Moldova and Transdniestr, a breakaway state where Russia has stationed troops since a short war in 1992.