"It should be drafted and adopted by the end of the year," Lutsenko told reporters.
Earlier in the day, the Ukrainian lawmaker wrote on Facebook that elections in areas that Kiev does not control must take place 90 days after the adoption of a special law on terms of holding elections in Donbass.
Ukraine is expected to hold elections October 25, while Donetsk and Luhansk plan their own local elections, October 18 and November 1, respectively.
Following the Normandy Quartet meeting, French President Francois Hollande and German Chancellor Angela Merkel announced that the sides agreed on the necessity to adjourn the election in Ukraine’s east.
On Monday, Russian Foreign Minister Sergei Lavrov said that Moscow was sending signals to the Donetsk and Lugansk people's republics to postpone their local elections and was waiting for their reaction.