"Financial losses have been preliminarily estimated at $1.2 billion, but that figure may not be final," Igor Sechin told President Dmitry Medvedev.
Kiev and Moscow have been embroiled in a bitter dispute over debt and gas prices for Ukraine in 2009, which led to Gazprom cutting off Europe-bound supplies earlier this month as it accused Ukraine of siphoning off the transit gas.
The European Union, where 18 states have been affected by energy shortfalls in freezing temperatures, has threatened to review ties with the two ex-Soviet countries and stepped up debate on alternatives to Russian gas.
European Commission President Jose Manuel Barroso has said the EU would advise its energy firms go to court if Moscow and Kiev failed to resolve their dispute shortly. Europe imports a quarter of its gas needs from Russia, and 80% of which is transited via Ukraine.
Serbia's gas company Srbijagas earlier announced plans to sue Ukraine's oil and gas firm Naftogaz over the disruption.
Ukraine, which has denied it steals gas intended for Europe, demands Gazprom provide technical gas above the contractual export volumes to ensure required pressure to pump energy to the EU.
Russia and major European gas utilities are discussing Moscow's proposal that a consortium of energy companies share the financial risks of supplying technical gas to Ukraine.
