Patriarch Kirill suggested a truce from noon on Friday to midnight on Saturday local time.
The Russian Orthodox Church, which uses the ancient Julian calendar, celebrates Christmas on January 7 although some Christians in Ukraine also mark the holiday on that date.
Ukrainian presidential adviser Mykhailo Podolyak dismissed Kirill's call as "a cynical trap and an element of propaganda".
President Volodymyr Zelenskiy had proposed a Russian troop withdrawal earlier, before December 25, but Russia rejected it.
Russian officials made no comment on Kirill's overture.
However, Russian President Vladimir Putin spoke by phone with Turkey's president on Thursday and the Kremlin said Putin "reaffirmed Russia's openness to a serious dialogue" with Ukrainian authorities.
But that professed readiness came with the usual preconditions: that "Kyiv authorities fulfil the well-known and repeatedly stated demands and recognise new territorial realities," the Kremlin said, referring to Russia's insistence that Ukraine recognise Crimea as part of Russia and acknowledge other territorial gains.
Previous attempts at peace talks have fallen at that hurdle as Ukraine demands that Russia withdraws from occupied areas at the very least.
Elsewhere, the head of the NATO military alliance said he detected no change in Russia's stance on Ukraine, insisting that the Kremlin "wants a Europe where they can control a neighbouring country".
"We have no indications that President Putin has changed his plans, his goals for Ukraine," NATO Secretary General Jens Stoltenberg said in Oslo.
Ukraine's allies have renewed a vow to keep supporting the country for as long as it takes to defeat Russia.
In the latest pledge of military help, the French Defence Ministry said it plans talks soon with its Ukrainian counterpart on delivering armoured combat vehicles.
France's presidency says it will be the first time this type of wheeled tank destroyer is sent to Ukraine's military.
Also, US President Joe Biden said Bradley Fighting Vehicles, a medium armoured combat vehicle that can serve as a troop carrier, could be sent to Ukraine.
The fighting in Ukraine has increasingly become a war of attrition in recent weeks as winter sets in.
Kyrylo Tymoshenko, deputy head of the Ukrainian presidential office, said on Thursday at least five civilians were killed and eight wounded across the country by Russian shelling in the previous 24 hours.
The ongoing intense battle for the eastern city of Bakhmut has left 60 per cent of the city in ruins, Donetsk governor Pavlo Kyrylenko said on Thursday.
Ukrainian defenders were holding the Russian forces back but the Kremlin's forces have pummelled the city with months of relentless shelling.
Taking the city in the Donbas region, an expansive industrial area bordering Russia, would not only give Putin a major battlefield gain after months of setbacks but it also would rupture Ukraine's supply lines and open the way for Russian forces to press on toward key Ukrainian strongholds in Donetsk.
