"This is an urgent task. We must resolve this task today," Alexei Miller told journalists after a meeting with European Parliament President Hans-Gert Pottering.
Miller also said Gazprom and the European Union have agreed in principle that independent observers will be dispatched to monitor Ukraine's gas transportation systems.
"We hope this decision will be made very promptly," he said.
Miller said German Chancellor Angela Merkel and Russian Prime Minister Vladimir Putin recently had a phone conversation, and Merkel proposed setting up an international committee of EU independent experts to control Russian gas flows to Europe through Ukraine.
"We fully support this initiative," he said.
Oleh Dubyna, the head of the Ukrainian energy company Naftogaz, said Thursday at a meeting with EU officials in Brussels over the Russia-Ukraine gas row that Ukraine is ready to guarantee Russian gas transit to Europe in full.
Dubyna also said that Ukraine is ready to allow EU experts into its territory for them to control Russian gas transit, including when the gas enters Ukraine and when it leaves the country.
Naftogaz spokesman Valentyn Zemlyanskiy said Thursday Gazprom CEO Alexei Miller and Dubyna could continue gas talks in Moscow later this week.
Previous talks between Russia and Ukraine ended on New Year's Eve with no agreement on how to settle Kiev's gas debts or on a contract for 2009 deliveries.
Gazprom halted on Wednesday gas supplies to Ukraine for transit to Europe. According to the company, the latest check established that Ukraine was not carrying any gas to Europe despite Russia's move to continue gas supplies to Ukraine through the Sudzha station.
Kiev closed on Wednesday the fourth, final gas pipeline pumping Russian gas to Europe. The latest closure added Austria, the Czech Republic, Romania and Slovakia to the growing list of countries receiving no Russian gas.
The three other pipelines were closed on Tuesday, ending deliveries via Ukraine to Hungary, Serbia, Macedonia, Croatia, Bulgaria, Turkey, Greece, and Bosnia and seriously disrupting supplies to Italy, Poland, France and Slovenia.
Gazprom earlier accused Ukraine of stealing more than 86 million cubic meters of gas since the start of the year, but Kiev denied the accusations saying that Russia was trying to discredit Ukraine as a reliable gas transit partner.
