Petro Poroshenko proposed scrapping a law, agreed under the September 5 truce deal, which gives special status to the eastern Donetsk and Luhansk areas.
Two pro-Russian leaders were declared the winners of Sunday’s polls.
Under the terms of the truce, Ukraine was meant to hold elections in the two regions in December.
The West says the rebel-held elections are illegal but Russia is backing them.
More than 4,000 people have been killed in fighting in eastern Ukraine since April.
Ukraine accuses Russia of arming the rebels and sending Russian regular troops across the border – a claim denied by Moscow.
Addressing the nation on TV late Monday, President Petro Poroshenko said he would hold a meeting of Ukraine’s Security and Defense Council on Tuesday to propose abolishing the law granting special self-government to rebel-held areas.
Petro Poroshenko described the November 2 “pseudo-elections” in Donetsk and Luhansk as a “farce at gunpoint” which would never be recognized as legitimate.
Sunday’s polls, he said, were “a gross violation” of the Minsk agreement – a roadmap to a peaceful settlement agreed by Ukraine, Russia, the Organization for Security and Co-operation in Europe (OSCE) and also rebel delegations.
“We demonstrated to residents of the Donetsk and Luhansk regions, as well as to the whole world, that we are sincere in our desire for political settlement,” he said.
“The militants refused this opportunity.”
Ukraine and the West have always insisted the rebel territories must abide by the Minsk deal and hold the local elections under Ukrainian law in December.
The US said it condemned the “illegitimate, so-called <<elections>> held on Sunday” and was “concerned by a Russian foreign ministry statement that seeks to legitimize [them]”.
EU foreign policy chief Federica Mogherini said the polls were “a new obstacle on the path towards peace”, while Germany said Russia’s backing of the vote was “incomprehensible”.
German Chancellor Angela Merkel’s spokesman, Steffen Seibert, warned Russia could face further sanctions as a result of its position.
Russia earlier said it respected “the will of the people of the south-east”. It called for a “sustainable dialogue” between the authorities in Kiev and the rebels.
Results released on November 3 showed Alexander Zakharchenko, the self-declared prime minister in Donetsk, had won the poll to become the head of the region. His party also came first in the parliamentary election.
In Luhansk, the incumbent rebel prime minister, Igor Plotnitsky, was declared the winner.
They are both expected to be officially sworn in later on Tuesday.
Both sides have repeatedly violated the ceasefire agreed in September.
The separatist insurrection erupted in the east after Russia annexed Ukraine’s southern Crimea peninsula, weeks after Ukraine’s pro-Russian President, Viktor Yanukovych, was forced out of office by mass protests in Kiev.
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