Supplies have already been cut off for a number days, with both sides blaming each other for the stoppage of shipments, as Europe suffers 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 European Union receives a quarter of its gas supplies from Russia, 80 per cent of which pass through Ukraine.
Supplies to 18 countries have been disrupted by the dispute.
Mirek Topolanek, the Czech prime minister, whose country holds the EU presidency, was due to travel to Ukraine on Friday to try to finalise agreement on the monitoring.
Obstacles to a deal remain, and the head of Naftogaz, Ukraine's state energy company, said talks over the last two days with Gazprom had made no progress.
Naftogaz also said Russia had not given Ukrainian monitors access to gas-pumping stations on Russian territory.
Gazprom also 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 only resume supplies to Europe via Ukraine once Kiev has formally signed a deal on the deployment of gas monitors.
Once the monitors are in place it could still take days before Russian gas shipped via Ukraine starts reaching Europe again.
|Russia has repeatedly said Ukraine must now pay the going market rate [AFP]
The gas is likely to be delivered only to Europe, not Ukraine itself, since Moscow and Kiev have yet to agree a price for the gas, which has been subsidised since Soviet times.
Russia has repeatedly said Ukraine must now pay the going market rate.
But the presence of monitoring missions at points along the transit routes for Russian gas will reassure Moscow that the gas it is pumping across Ukraine 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 gas 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, while the continent faced freezing winter temperatures.
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 gas supplies earlier this week.
Turkey and Serbia, also hit hard by the gas dispute, were receiving extra shipments from Iran and Hungary.