People living in the separatist regions will now be entitled to receive a Russian passport within three months of applying for one.
Importantly, Nebenzia noted that applicants for Russian citizenship and travel documents can keep their Ukrainian citizenship.
The decree was aimed at residents of the unrecognised Donetsk and Lugansk republics that broke away from Kiev in 2014 and are governed by Moscow-backed rebels.
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Kiev launched a military operation against the DPR and LPR in 2014 after they proclaimed independence from Ukraine, refusing to recognize the new central government that was installed via a coup d'etat.
Poroshenko was elected in May 2014, after Moscow-friendly President Viktor Yanukovych was pushed from power that February by a protest movement known as the Maidan after he scrapped plans for closer ties with the European Union and vowed to boost trade with Russian Federation.
Despite this agreement, however, sporadic fighting continues in Donbas.
Ukraine said it had informed the United Nations about Russia's move and also asked the European Union to take "prompt and decisive" action.
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Speculations about expedited citizenship for the Donetsk and Luhansk regions were swirling in Russian Federation throughout the Ukrainian presidential campaign, but it had appeared that the Kremlin was only intending to go through with it if the incumbent leader, Petro Poroshenko, had won.
According to Russia's Interfax news agency, the reaction in Ukraine prompted Putin to say that he did not want problems with the new government, but instead was concerned about human rights in the area.
Speaking on condition of anonymity because of the sensitivity of the subject, a Western diplomat involved in negotiations related to the conflict in eastern Ukraine told RFE/RL that Putin's decree is "a highly provocative step that undermines efforts to deescalate the situation" in the Donbas. "The same method was used with Abkhazia and South Ossetia".
Mr Zelensky was elected as Ukraine's next president at the weekend with no previous political experience except playing the role of president in a comedy television show.
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