Bulgaria and Macedonia also reported that all supplies of Russian gas had been cut, while Romania's pipeline operator said that its supplies had been cut by 75 per cent.
Bulgaria's finance ministry said the country was facing a crisis. Petar Dimitrov, the economy and energy minister, said: "Russia and Ukraine must find an urgent solution because the energy systems of dozens of countries are at risk."
The European Commission condemned the cuts as "completely unacceptable". In an unusually strongly worded statement, it demanded that Russia restore supplies "immediately".
Russia ordered a reduction in gas flow to Europe via Ukraine on Monday, a measure it said was to stop its neighbour from stealing fuel. Ukraine said the move would jeopardise supplies to the rest of Europe, which is facing freezing temperatures.
The gas row has raised new questions about Russia's reliability as an energy supplier. Moscow and the state energy giant Gazprom will come under increasing pressure this week from the European Union to revolve their differences with Kiev over gas prices and allegations that it has siphoned off supplies intended for the EU.
Martin Riman, the Czech industry and trade minister and a member of an EU delegation visiting Kiev, said the energy situation had "changed very dramatically" overnight and is "getting worse".
"The situation changed very dramatically. The amount of gas transported from Russia to Ukraine decreased and the situation of the Slovakian border is getting worse," he said.
A key pipeline for the exports of Russian gas to Europe crosses the border from Ukraine into EU member Slovakia.
Olexander Shlapak, deputy chief of Ukraine's presidential secretariat, said that Russia had "crudely violated agreements" with its reduction in gas deliveries.
The Ukrainian state gas firm Naftogaz said that Russia had slashed Europe-bound gas deliveries via Ukraine by nearly 60 per cent.
The dramatic reduction came after Vladimir Putin, the Russian prime minister, ordered Gazprom to cut deliveries through Ukraine with immediate effect on Monday.
The crisis began on Jan 1 when Gazprom began to cut gas deliveries to Ukraine's domestic market, claiming that Kiev owed it more than $2 billion (£1.36 billion) in unpaid bills and late-payment fines.
Russia halts gas supplies to European countries