The billionaire chocolate baron was backed by 44.6 per cent of respondents polled on May 14-18 by two respected Ukrainian agencies whose surveys receive EU financial support.
The figure is just short of the 50 per cent threshold the 48-year-old needs to break to avoid a June 15 runoff, leaving Ukraine in the hands of an interim leadership that lacks recognition from Russia even as the death toll climbs in clashes across the separatist east.
The survey showed Poroshenko easily beating Tymoshenko in the runoff, with 52.2 per cent of respondents backing his candidacy.
Only 9.9 per cent said they would vote for the ex-premier, with the rest either undecided or saying they had no intention of voting.
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The poll pointed to a high turnout, with 60 per cent saying they would definitely turn out for the election and another 19 per cent suggesting they would probably do so.
Russia, facing the threat of further Western sanctions should it interfere in the election, has grudgingly backed the ballot without saying outright that it will recognise the winner.