Oleksandr Turchynov, the secretary of Ukraine's national security council, said Russia's move was meant to give Moscow legal cover for deploying its troops to eastern Ukraine on the pretext of protecting Russian citizens.
Five years of war between Ukrainian troops and Russian-backed forces have killed 13,000 people despite a notional ceasefire signed in 2015.
Russia is not forcing residents of the Donbas region to change their citizenship, but to have the option of applying for Russian citizenship without losing their Ukrainian one, Russian Ambassador to the United Nations Vassily Nebenzia said during a UN Security Council meeting.
Outgoing President Petro Poroshenko on Twitter called the vote a "historic event", comparing it to the regeneration of the Army and the creation of a unified Ukrainian Orthodox church.
"Ukraine's new leadership can not fail to understand this", he said.
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European Commission spokeswoman Maja Kocijancic said Thursday the fact that Putin's move came just days after presidential elections in Ukraine "shows Russia's intention to further destabilize Ukraine and to exacerbate the conflict".
His press service said in a statement that Kiev is 'counting on increased diplomatic and sanctions pressure on the Russian Federation'.
"This is an attempt to justify and legitimize Russia's military presence in the occupied part of the Ukrainian Donbass", Poroshenko said in a video statement, referring to the Kremlin-backed separatist areas.
The Ukrainian ambassador to the UN, Volodymyr Yelchenko, said on Twitter that his country would be asking the UN Security Council to prohibit Russian Federation from enacting the decree in the ex-Soviet republic. Separatist authorities said Wednesday that they had issued about 300,000 such ID cards in the area with an estimated population of 3.7 million. Putin, however, unlike other world leaders, has not yet congratulated him on his victory, saying that the election results are not yet final.
During the campaign, Zelenskiy did not sound as bellicose as his predecessor and said he wanted a peaceful resolution of the conflict.