DONETSK, Ukraine (AFP) - Voting began on Sunday in referendums called by pro-Russian rebels in eastern Ukraine to split from the rest of the ex-Soviet republic, polls the US slammed as "illegal" as the West fears they could spark civil war.

The vote, carried out as two "referendums" in provinces where the insurgents hold more than a dozen towns, marks a serious deepening of the political crisis in Ukraine, which has pushed East-West relations to lows not seen since the end of the Cold War.

Although a "yes" vote would likely be recognised only by Russia, it would greatly undermine a presidential election Ukraine is to hold in two weeks, which the United States and the European Union see as crucial to restoring stability.

And they come as fighting continued in eastern Ukraine, with several explosions heard overnight in the flashpoint town of Slavyansk as the Kiev authorities try to flush the rebels from towns they control.

Troops have been battling the well-armed separatists, who have barricaded themselves in towns and cities in the two provinces where the votes are taking place: Donetsk and Lugansk.

The referendums are "illegal under Ukrainian law and are an attempt to create further division and disorder," US State Department spokeswoman Jen Psaki said in a statement late Saturday.

The votes "violate international law and the territorial integrity of Ukraine," she stressed, adding that the United States would not recognise the result.

Earlier Saturday, France and Germany jointly threatened "consequences" on Russia if the presidential election is scuppered - echoing US President Barack Obama's warning of automatic sanctions that would slice into whole sectors of Russia's weakening economy.

Interim Ukrainian president Oleksandr Turchynov warned that voting for independence would be a "step into the abyss" for these regions and lead to the "total destruction" of the economy there.

'100 PERCENT TURNOUT'

Despite rebel claims that the polling will reach 90 per cent of the seven million people living in these two provinces, the areas they hold account for less than half that population.

They decided to go ahead with the vote despite a public request made Wednesday by Russian President Vladimir Putin to postpone it.

Polling stations opened in schools in rebel-held territory at 8:00 am (2:00 pm, Singapore time) and were to close 12 hours later, according to insurgent chiefs in the city of Donetsk.

The self-proclaimed mayor of Slavyansk, Mr Vyacheslav Ponomaryov, said he expected 100 per cent turnout for Sunday's vote.

After the results come in, "the Republic of Donetsk will begin to function" and cultivate "friendly relations" with Russia, he added.

But another rebel leader, Mr Roman Lyagin, said: "If the answer is yes, it does not necessarily mean that we will be joining Russia".

A poll released Thursday by the Pew Research Centre in the United States suggested 70 per cent of Ukrainians in the east want to stay in a united country, while only 18 per cent back secession.

Kiev has already dismissed the vote as "illegitimate" and against the Ukrainian constitution.

However, like in Crimea - which Russia annexed in March after a similar referendum - it has been powerless to stop preparations.

One voter, Viktoria Petrovna, arrived early in the city of Donetsk to cast her vote, telling AFP: "This is an important day. They told us to come and vote, so it's essential to do that." "We are living in very important times."

WEST THREATENS 'CONSEQUENCES'

The Ukrainian government and its Western backers accuse Mr Putin of deploying Russian special forces in east Ukraine, as in Crimea, to see the vote through and to sabotage the May 25 presidential election.

Mr Putin belatedly admitted sending military forces to Crimea but continues to deny militarily meddling in east Ukraine.

Ms Psaki said that "we still see no Russian military movement away from the border" despite Putin's claim that Russian forces were pulling back.

In their joint statement Saturday, French President Francois Hollande and German Chancellor Angela Merkel urged Ukraine's security forces to stop their offensive on rebel-held positions in order to give dialogue a chance.

That echoed a call by Mr Putin, who set that as his condition for backing the presidential election.

But, the leaders of France and Germany warned, if the subsequent presidential election was stymied, "appropriate consequences should be drawn", indicating tougher sanctions in line with those brandished by the United States.

The vote added fuel to a crisis that has turned increasingly deadly in the past two weeks.

On Friday, up to 21 people were killed in what Interior Minister Arsen Avakov said was a "full-scale military clash" in the southeastern port city of Mariupol. The violence occurred as Ukraine and Russia commemorated the Soviet victory over German forces in World War II - during which Putin made a triumphant visit to annexed Crimea.

Mariupol on Sunday observed a day of mourning, and an AFP reporter said passions remained high.

Although the death toll there varied, according to different officials, it appeared to be the bloodiest day in the conflict since May 2, when clashes that resulted in a horrific inferno in the southern port city of Odessa claimed another 42 lives, most of them pro-Russian activists.