DONETSK, Ukraine - Swathes of eastern Ukraine controlled by pro-Russian rebels voted on independence Sunday in polls the West slammed as illegal amid fears they could fan violence into full civil war and lead to the break-up of the ex-Soviet republic.Fighting flared anew on the outskirts of the flashpoint town of Slavyansk where rebels tried to seize back a local television tower from Ukrainian troops. Tensions were high elsewhere. But in the centre of Slavyansk and surrounding towns, voters lined up calmly to cast ballots on self-rule for their two provinces, being asked to answer 'yes' or 'no' to the question: ‘Do you approve of independence for the People's Republic of Donetsk?’ and for neighbouring Lugansk. ‘I want to be independent from everyone,’ said ex-factory worker Nikolai Cherepin as he voted yes in the town of Mariupol, in Donetsk province. ‘Yugoslavia broke up and they live well now’. Nikolai Somtsev, the deputy chief of the self-styled electoral commission in Donetsk city, said ‘everything is organised very well’ and was taking place as planned.Kiev has dismissed the so-called ‘referendums’ addressed to seven million of Ukraine's total 46 million inhabitants as illegitimate and unconstitutional. Its Western backers echo that, but are concerned a ‘yes’ result could scupper plans for a nationwide May 25 presidential elections seen as crucial for restoring stability.Russian President Vladimir Putin has publicly distanced himself from Sunday's vote, making an appeal for it to be postponed, but was ignored by the rebels. The United States and the European Union still see Putin's hand in the unrest that has gripped eastern Ukraine since early April, believing he is seeking a re-run of the scenario that ended up with him annexing Crimea in March.If Ukraine's presidential election in two weeks is stymied, the United States and Europe have warned of automatic sanctions designed to cripple broad sectors of Russia's economy. The Ukraine crisis has already pushed East-West relations to their lowest point since the Cold War. Ukrainian troops have been battling the well-armed separatists, who have barricaded themselves in the more than dozen towns and cities they have grabbed. In Mariupol, scene of recent fierce fighting between Ukrainian troops and pro-Russian militants, queues of hundreds of people snaked towards the polling stations, an AFP reporter on the scene said.Tatiana, a 35-year-old florist voting in the regional hub of Donetsk, told AFP: ‘We have come to fight for our rights and become independent and we are happy that we've been given the right to voice our opinion.’ ‘If we're independent, it will be hard at the beginning but it will be better than being with the fascists,’ she added, using a term frequently used by separatists to describe the Western-backed government in Kiev.But not all voters seemed to grasp the implications of the poll. ‘The Donetsk People's Republic will not be separate, it will remain as part of Ukraine but it will become autonomous, as far as I understand,’ said Irina, a children's dentist casting her ballot in Donetsk.Ahead of the referendums, US State Department spokeswoman Jen Psaki said they were ‘illegal under Ukrainian law and are an attempt to create further division and disorder’. She added that the United States would not recognise the result. On 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. Polling stations opened in schools in rebel-held territory at 8:00 am (0500 GMT) and were to close 12 hours later, according to insurgent chiefs in the city of Donetsk.The self-proclaimed mayor of Slavyansk, Vyacheslav Ponomaryov, said he expected 100 percent 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, 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 percent of Ukrainians in the east want to stay in a united country, while only 18 percent back secession. The vote added fuel to a crisis that has turned increasingly deadly in the past two weeks. On Friday, several people were killed in what Interior Minister Arsen Avakov said was a ‘full-scale military clash’ in the southeastern port city of Mariupol, as Ukraine and Russia commemorated the Soviet victory over German forces in World War II.Moreover, French President Francois Hollande on Sunday denounced separatist votes by pro-Russian rebels in eastern Ukraine as ‘null and void’. On a visit to the ex-Soviet republic of Azerbaijan, Hollande said the votes taking place in Donetsk and Lugansk made ‘no sense’ and that ‘the only election that will count’ will be Ukraine's presidential vote on May 25.