France, Italy, Germany and Poland were among those reporting falling volumes.
Russia said it was sending an extra 95 cubic metres a day to make up for gas "stolen" by Ukraine.
Russian gas monopoly Gazprom raised the price of 1,000 cubic metres of gas from $50 to $230 and Ukraine refused to pay.
Moldovan President Vladimir Voronin said his country had also been cut off, after refusing to pay $160 per 1,000 cubic metres, according to the Itar-Tass news agency.
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.
The EU's foreign policy chief Javier Solana urged Kiev and Moscow to resume negotiations, as EU energy officials prepared to discuss the crisis at a meeting on Wednesday.
Germany, which depends on Russia for 30% of its supplies, has called on Moscow to "act responsibly".