European Energy Commissioner Gunther Oettinger met with Russian Energy Minister Alexander Novak and his Ukrainian counterpart, Yuri Prodan, to settle lingering issues in the Ukrainian natural gas sector.
The European Commission said Monday "substantial progress" has been made, though there were no major breakthroughs.
Russian energy company Gazprom said Ukraine would have to pay in advance for natural gas unless it settles a multi-billion dollar gas bill.
Ukraine hosts the bulk of Russia's gas delivered for Europe and the stalemate has put the region's energy security at risk.
The European Commission said Ukrainian energy company Naftogaz agrees to pay $2 billion by Friday and another $500 million by June 7 to settle its outstanding debts.
"Gazprom agrees to continue to supply gas for June without insisting on prepayment [upon receipt]," a proposed deal stipulates.
The European Commission said another round of talks is set for Friday in case all parties to the proposed agreement fail to reach a deal.