Two polls gave Poroshenko, a billionaire businessman with long experience in government, 55.9 to 57.3 percent, well ahead of former prime minister Yulia Tymoshenko, in second place with just over 12 percent. If confirmed by results on Monday, there will be no need for a runoff vote on June 15.
Poroshenko, set to be the new president after the Sunday election, said there should also be a parliamentary election this year.
"All the polls show that the election has been completed in one round and the country has a new president," said the burly 48-year-old.
However, in the eastern Donbass coalfield, where militants ensured polling stations were closed to some 10 percent of the national electorate, rebels scoffed at the "fascist junta" and announced a plan to "cleanse" their "people's republic" of "enemy troops". A minister in Kiev said in turn its forces would renew their "anti-terrorist operation" after a truce during the polling.
More than 20 people were killed in the region last week.
Asked about relations with Russia, Poroshenko said the "sovereignty and territorial integrity" of Ukraine were paramount for him.
At his campaign headquarters, he told supporters the majority of Ukrainians had given him a mandate to continue a course of integration with the rest of Europe but said his first priority was to travel to the east of the country to end "war and chaos" caused by pro-independence rebels.
NTJ/MB