Local Russian leaders wrote a letter to President Vladimir Putin, urging him to end the mobilization of reservists.
Officials have said the draft is "complete," but the letter asks Putin to codify this with a decree.
Both are party deputies for the liberal Yabloko political party — which opposes the war in Ukraine — in the northwestern Russian region of Karelia.
Putin's press secretary, Dmitry Peskov, told Russian news wire RIA Novosti on Wednesday that he hasn't seen the deputies' letter.
In the meantime, Anton Gerashchenko, an advisor to the Ukrainian Internal Affairs minister, accused Russia of preparing to draft 500,000 to 700,000 new reservists in January.