EU foreign policy chief Javier Solana said he was trying to persuade both sides to resume talks. Ukraine said it would call for arbitration.
Russia says it will pump more gas to countries that said supplies had fallen after Moscow cut Kiev's provision.
Gas firm Gazprom said full supply would be restored by Wednesday evening.
EU energy officials are set to discuss the crisis at a meeting on Wednesday.
France, Germany, Poland, Italy and Slovakia all reported drops in supply through pipelines running through Ukraine.
Austria and Hungary, which were also affected, said on Tuesday that the flow of Russian gas had returned to normal levels.
Russia says it is sending an extra 95m cubic metres a day to make up for gas "stolen" by Ukraine.
Ukraine denies it has siphoned off $25m (£15m) worth of gas from a pipeline crossing its territory after Russia cut off its supply.
Gas Cut Impact
-- Ukraine - loses 100% of Russian imports
-- Austria and Hungary - Russian imports down, now restored
-- Poland - supply down 14% on Sunday. Seeking to increase supplies from alternative pipe
-- Slovakia and Romania - supplies down by a third
-- Germany - says supplies have fallen, but did not quantify
-- France - heavy user of Russian gas. Has reported 25-30% drop in supply
However, Kiev says it has the right under existing contracts to take a share of gas exported via the Ukrainian pipeline - the main route for Russian exports - and would do so if the temperature fell below -3C.
The dispute started when state-owned Gazprom raised the price of 1,000 cubic metres of gas from $50 to $230 and Ukraine refused to pay.
Gazprom is still charging the lower price to some former Soviet countries, though the average price in the EU is $240.
Moldova says it was also cut off after refusing to double what it paid to $160 for 1,000 cubic metres.
European Union energy commissioner Andris Piebalgs told the BBC's World Tonight programme that he was monitoring the situation and invited Russia and Ukraine to resume negotiations.
He said nobody was to blame, but that the situation was complex.
"Ukraine is definitely not able to pay a four times increase of price. It is just not possible if you pay $50... and the next day you should pay $230. You just can't do it," he said.
Kiev says it is being punished for its attempts to become more independent from Moscow and develop stronger ties with the West.
It has accused Russia of resorting to blackmail in order to undermine Ukraine's economy.
Relations between Russia and Ukraine have been tense since Mr Yushchenko came to power last year on a promise to strengthen relations with the EU and Nato, and steer the country out of Russia's sphere of influence.
Ukraine says it is not opposed to an increase in gas prices, if this is phased in gradually, and says taps should be turned back on while negotiations continue.
Gazprom's European Trade
One-third of EU gas imports, and one-fifth of gas used in EU. Ukrainian pipeline network carries 90% of Gazprom's exports to West and Central Europe.
Big customers (2004)
Germany - 38bn cubic metres; Ukraine - 34bn; Italy - 21bn; Turkey - 14bn; France - 12bn
Dependence on Ukrainian pipeline
Slovakia - 100% of gas consumed is from Russia; Bulgaria - 94%; Greece - 92%; Czech Rep - 73%; Hungary - 72%; Austria - 63%; Poland - 60%
Work is under way to boost capacity of pipeline via Belarus to Poland - in 2006 it could reach 33bn cubic metres per year. A pipeline also carries Russian gas under the Black Sea to Turkey (16bn cubic metres). Plans exist for a Baltic Sea pipeline, which in 2010 would carry 27bn cubic metres per year to Germany.
Source: BBC News