Martin Riman, the Czech industry and trade minister, said Russian gas supplies to Europe can resume from Sunday.
"Gas supplies can resume Sunday if everyone works at 100 per cent," Riman said after the Topolanek-Tymoshenko talks.
Earlier Russia and the European Union signed a similar deal that would allow EU, Ukrainian and Russian observers to monitor gas supplies flowing through Ukraine.
"As soon as the control mechanism comes into effect, we will open the gas system," Vladimir Putin, the Russian prime minster, said.
"But we will watch how much gas goes into Ukrainian territory and how much comes out.
"If we see theft and any part of the gas is lost, we will again cut delivery by that amount."
Moscow cut off gas shipments that flowed through Ukraine more than a week ago after accusing Kiev of siphoning off supplies for its own use.
Gas price row
Direct negotiations between Russia and Ukraine had faltered overnight after hours of debate.
| Putin, the Russian prime minister, said Ukraine had brought a 'gas blockade' to Europe [AFP]
The dispute first broke out when Moscow and Kiev failed to agree on the price for gas for the coming year.
Russia had insisted Ukraine pay current market rates instead of the subsidised prices introduced during the Soviet era that it had been paying.
The two countries have also clashed over Ukraine's efforts to join Nato.
Supplies to 18 countries have been disrupted by the dispute and factories in eastern Europe have been forced to close.
Europe receives a quarter of its gas from Russia, 80 per cent of which passes through Ukraine.
When it resumes, gas is likely to be delivered to Europe alone and not Ukraine, as Moscow and Kiev have still not agreed on price.
The nine-day crisis has left hundreds of thousands of people in the Balkans without gas.
The Czech Republic said on Friday it would provide about four million cubic metres of gas per day to its neighbour Slovakia, which declared a state of emergency over its supplies earlier this week.
Turkey and Serbia, also hit hard by the gas dispute, were receiving extra shipments from Iran and Hungary.