EU foreign policy chief Federica Mogherini says the bloc considered the polls in Donetsk and Lugansk to be "illegal and illegitimate and will not recognise them."
More than a 100,000 people attended a memorial service on Sunday for a separatist leader in Ukraine who was killed in a blast two days ago.
Russia's Foreign Ministry said on Friday it had every reason to believe Kiev was responsible for the death of eastern Ukraine rebel leader Alexander Zakharchenko.
Alexander Zakharchenko was killed in an explosion in a cafe in the Donetsk region's capital.
The bill describes the areas in the Ukraine's Donetsk and Luhansk regions as "temporarily occupied" by "aggressor country" Russia.
Vodafone is the largest mobile provider in eastern Ukraine but its fibre optic line was cut. The company says it needs reassurances from the warring parties to repair the damage.
The Russian president spoke with separatist leaders Aleksandr Zakharchenko of the Donetsk region and Igor Plotnitsky of Luhansk about swapping 306 rebels imprisoned by Kiev for 74 people jailed by the separatist republics before Christmas.
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