"If we see theft and any part of the gas is lost, we will again cut delivery by that amount."
The monitoring systems are not expected to be put in place until Ukraine also signs the deal.
Mirek Topolanek, the Czech prime minister, whose country holds the EU presidency, told his Russian counterpart that they should sign and "we will go immediately to Kiev to ask the same of the Ukrainian side".
"We will end the crisis," he said.
Gas price row
Direct negotiations between Russia and Ukraine had faltered overnight after hours of debate.
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.