Russian President Vladimir Putin has warned European leaders that Ukraine's delays in paying for Russian gas have created a "critical situation".
Pipelines transiting Ukraine deliver Russian gas to several EU countries and there are fears that the current tensions could trigger gas shortages.
Pro-Russian separatists are holed up in official buildings in Donetsk and Luhansk, eastern Ukraine.
Meanwhile, a European human rights body has stripped Russia of voting rights.
The Parliamentary Assembly of the Council of Europe (PACE) monitors human rights in 47 member states, including Russia and Ukraine.
Protesting against Russia's annexation of Crimea last month, PACE suspended Russia's voting rights as well as Russian participation in election observer missions.
The Russian delegation had boycotted the meeting. Its leader, Alexei Pushkov, described the proceedings as a "farce".
Russian state gas giant Gazprom says Ukraine's debt for supplies of Russian gas has risen above $2bn (£1.2bn; 1.4bn euros).
Gazprom said on Wednesday it could demand advance payments from Kiev for gas but President Putin said the company should hold off, pending talks with "our partners" - widely believed to mean the EU.
In a letter to European leaders, President Putin warned that the "critical" situation could affect deliveries of gas to Europe, his spokesman Dmitry Peskov said.
The letter released by the Kremlin says that if Ukraine does not settle its energy bill, Gazprom will be "compelled" to switch over to advance payment, and if those payments are not made, it "will completely or partially cease gas deliveries".
Mr Putin adds that Russia was "prepared to participate in the effort to stabilise and restore Ukraine's economy" but only on "equal terms" with the EU.
And he says that while Russia has been subsidising the Ukrainian economy with cheap gas, Europe has been exploiting its raw materials and worsening its trade deficit.
The US state department later said it condemned "Russia's efforts to use energy as a tool of coercion against Ukraine".
Spokeswoman Jen Psaki said the price Ukraine was being charged for its gas was "well above the average price paid by EU members".
Nearly a third of the EU's natural gas comes from Russia.
Previous Russian gas disputes with Ukraine have led to severe gas shortages in several EU countries. The EU says it has extra gas supplies and reverse-flow technology to deal with any such disruption now.
In Kiev, the authorities said Ukraine would not prosecute pro-Russian activists occupying official buildings in Donetsk and Luhansk if they surrendered their weapons.
The separatists in the east - a mainly Russian-speaking region with close ties to Russia - are demanding referendums on self-rule. In Donetsk they have declared a "people's republic". Gunmen have been seen among the protesters in Luhansk.
Ukraine has accused Russia of stirring up the unrest, a claim Moscow denies.
Meanwhile, Nato has unveiled satellite images it says show some 40,000 Russian troops near the Ukrainian border in late March and early April, along with tanks, armoured vehicles, artillery and aircraft.
British Brigadier Gary Deakin, speaking at Nato military headquarters in Belgium, said it was a force that was "very capable, at high readiness, and... close to routes and lines of communication".
A Russian military officer said the images dated from August last year and denied there had been a build-up of troops along the border, Russia's Ria Novosti news agency reported.
Ukraine fears that the Russian separatist actions are a provocation similar to the protests that gripped Crimea days before Russian troops annexed the peninsula last month. Russia denies the claim.
President Putin said on Thursday his decision to annex Crimea was taken after secret opinion polls and had not been planned in advance.
Speaking to political supporters near Moscow, he said the first poll showed 80% of the Crimean population wanted to join Russia. He said he had not made any decision until it was "clear what the mood of the people was".
Russia, the US, Ukraine and the EU are to hold talks in Geneva next Thursday to try to resolve the impasse, EU diplomats have said.
They will be the first four-way talks since the crisis began.
Russian Foreign Minister Sergei Lavrov told US Secretary of State John Kerry by telephone on Wednesday that the meeting should focus on fostering dialogue among Ukrainians and not on bilateral relations among the participants.
In another development, the Kremlin announced that President Putin had sacked 14 generals. They were sacked from the emergencies ministry and prison service, as well as regional branches of the interior ministry and the Investigative Committee (Russia's equivalent of the FBI).
It was not immediately clear if the move was a routine step. Russia has some 800 generals in its army alone.