Gazprom said Kiev had on Monday signed the deal on deploying monitors to ensure smooth gas transit, dropping conditions which Moscow had earlier rejected as a "mockery of common sense."
Supplies have been cut off for nearly a week in freezing temperatures.
A Gazprom source said the firm's chief executive was on his way to Brussels. A source in Brussels said Russia's top energy official Igor Sechin was flying there too.
"The deal needs to be re-signed anyway by all parties. Only then monitors will start arriving at gas compressor stations and gas will resume flowing," a Gazprom source told Reuters.
Miller and Sechin were the two Russian signatories to the original monitoring deal.
Ukraine, its own supplies cut off in a dispute with Moscow over the price it pays for Russian gas, signed an agreement on Sunday allowing monitors to check gas flows across its territory to Europe and to address Russian fears that Kiev siphons off gas for itself.
But Kiev appended its own declaration to the deal, which Russia had signed a day earlier.
Russian President Dmitry Medvedev appealed to EU leaders late on Sunday to exert influence on Kiev to withdraw the annotations.
Russia has said it will turn the taps on only when the gas monitoring deal is signed by all sides and monitors are deployed.
Gazprom and Ukraine has said it will take at least 36 hours before gas reaches EU borders after flows resume, which means most countries will not get Russian gas before Wednesday.
The commercial dispute over gas prices has played out against a background of broader tensions between Ukraine, which is seeking to join the NATO alliance, and its giant eastern neighbor.
The EU gets a fifth of all its gas supplies from pipelines that run from Russia and then across Ukraine.
Eastern and central Europe have borne the brunt of the gas supply disruptions, with Bulgaria shutting schools because it could not heat them and Slovakia saying it would re-start a nuclear reactor which it shut down last year.
By Christian Lowe and Dmitry Zhdannikov
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