"We hope that things will now move quickly and constructively and that the Ukrainian side will abide by the agreement that it has so far accepted only in words," Miller said.
An EU monitoring team arrived in Kiev, Ukraine's capital, on Friday but, even if a final deal is signed, it is expected to take several days before new shipments reach Europe.
Supplies have been halted for a number days, with both sides blaming each other for the stoppage, as Europe experiences bitter winter weather.
Miller said: "We expect that, in the course of today, the protocol on the creation of an international independent mechanism to guarantee the transit of Russian gas through Ukraine will be signed and, immediately after that, we will renew [gas] deliveries."
The EU receives a quarter of its gas from Russia, 80 per cent of which passes through Ukraine. Supplies to 18 countries have been disrupted by the dispute.
Mirek Topolanek, the Czech prime minister, whose country holds the EU presidency, travelled to Ukraine on Friday to try to finalise the monitoring agreement.
Naftogaz, Ukraine's state energy company, says Russia had not given Ukrainian monitors access to gas-pumping stations on Russian territory.
Gazprom said Ukraine has previously been refusing to include Gazprom members in the international monitoring team.
In a meeting with Dmitry Medvedev, Russia's president, earlier on Friday, Miller said Gazprom would resume supplies to Europe via Ukraine only once Kiev has formally signed a deal on the deployment of gas monitors.
|Russia has repeatedly said Ukraine must now pay the going market rate [AFP]
Gas is likely to be delivered to Europe alone and not Ukraine, since Moscow and Kiev have still not agreed a price for the gas, which has been subsidised since Soviet times.
Russia says Ukraine must now pay the market rate.
But the presence of monitors along the transit routes will reassure Moscow that the gas is not being siphoned off by Kiev.
Moscow had cited the allegation, denied by Ukraine, as its reason for shutting off gas through its neighbour earlier this week.
The nine-day crisis has left hundreds of thousands of people in the Balkans without gas, forced factories to shut down and disrupted deliveries as far west as France and Germany.
The Czech Republic said on Friday it will 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.