(Adds details on Obama-Merkel call, paragraphs 8, 21-22)
* Putin says cut-off of gas to Ukraine possible
* Says gas supplies to Europe could be affected
* U.S. accuses Moscow of using energy as "tool of coercion"
* Ukraine stand-off with pro-Russian rebels deepens
By Alexei Anishchuk and Bill Trott
MOSCOW/WASHINGTON, April 10 (Reuters) - President Vladimir Putin warned on Thursday that Russian gas supplies to Europe could be disrupted if Moscow cuts the flow to Ukraine over unpaid bills, drawing a U.S. accusation that it is using energy "as a tool of coercion".
In a letter to the leaders of 18 European countries, Putin made clear that his patience would run out over Kiev's $2.2 billion gas debt to Russia unless a solution could be brokered urgently.
Russia has nearly doubled the gas price it charges Ukraine, whose economy is in crisis, since pro-Moscow President Viktor Yanukovich was overthrown two months ago. Russia then annexed the Ukrainian region of Crimea, provoking the biggest confrontation with the West since the Cold War.
Putin said Russian exporter Gazprom would demand advance payment for gas supplies to Ukraine and "in the event of further violation of the conditions of payment will completely or partially cease gas deliveries".
That could have knock-on effects for European Union countries, much of whose Russian gas flows in pipelines across Ukraine. "We fully realise that this increases the risk of (Ukraine) siphoning off natural gas passing through Ukraine's territory and heading to European consumers," the letter said.
Russia meets 30 percent of Europe's natural gas demand and half of this goes through Ukraine.
The United States accused Moscow of using its vast energy reserves to pressure the former Soviet republic. "We condemn Russia's efforts to use energy as a tool of coercion against Ukraine," State Department spokeswoman Jen Psaki said.
U.S. President Barack Obama, in a phone call on Thursday with German Chancellor Angela Merkel, "underscored the need for the United States, European Union and other global partners to be prepared to meet further Russian escalation with additional sanctions," the White House said.
State-controlled Gazprom stopped pumping gas to Ukraine during price disputes in the winters of 2005-2006 and 2008-2009, leading to reduced supplies in European countries.
Russian officials say gas dealings with Ukraine are purely commercial and it was forced to move after Kiev failed to meet a deadline on Monday to pay for its March supplies.
In Ukraine, pro-Russian separatists occupying two official buildings in the eastern cities of Donetsk and Luhansk rejected a government offer of an amnesty in exchange for laying down their weapons.
That raised fears that the authorities could follow through on a threat to use force to clear the buildings that have been occupied since last weekend.
Protesters wearing bullet-proof vests and armed with Kalashnikov rifles in a former KGB headquarters in Luhansk said they would lay down their weapons only if Kiev agreed to hold a referendum on the future of the largely Russian-speaking region.
Crimea voted last month for union with Russia in a referendum held after Moscow's forces had already taken control of the Black Sea peninsula. Kiev has rejected holding a similar vote in the east, saying the occupations are part of a Russian-led plan to dismember the country.
"We are trying to find a compromise, but the demands put forward by the occupiers are unacceptable. Our aim is to avoid the use of force, but that option remains in place," Deputy Interior Minister Serhiy Yarovy told journalists.
Prime Minister Arseny Yatseniuk is to travel to Donetsk on Friday to discuss the crisis.
NATO raised Moscow's ire by publishing satellite pictures it said showed a Russian military buildup on the Ukrainian border. Moscow said they had been taken last year.
"The alliance is trying to use the crisis in Ukraine to rally its ranks in the face of an imaginary external threat to NATO members and to strengthen demand for the alliance," the Russian Foreign Ministry said in a statement.
NATO Secretary-General Anders Fogh Rasmussen, visiting Prague, said the threat was real. "Russia is stirring up ethnic tensions in eastern Ukraine and provoking unrest," he told a news conference.
"And Russia is using its military might to dictate that Ukraine should become a federal, neutral state. That is a decision which only Ukraine as a sovereign state can make."
Obama and Merkel in their conversation called again on Moscow to move its troops back from the border region.
The White House said pro-Russian separatists, "apparently with support from Moscow," were destabilizing Ukraine through "an orchestrated campaign of incitement and sabotage."
A Pentagon representative confirmed that the destroyer USS Donald Cook arrived in the Black Sea on Thursday for exercises with ships from Romania, Bulgaria and Turkey.
U.S. Treasury Secretary Jack Lew told his Russian counterpart on Thursday the United States stood ready to impose additional sanctions on Russia if it continued to step up tensions, according to a Treasury representative. (Writing by Conor Humphries and Peter Cooney; Additional reporting by Steve Gutterman, Vladimir Soldatkin and Gabriela Baczynska in Moscow; Jason Hovet in Prague; Michelle Martin in Berlin; Adrian Croft in Mons, Belgium; Thomas Grove in Luhansk, Ukraine, Natalia Zinets in Kiev, and Timothy Ahmann, Steve Holland and Roberta Rampton in Washington; Editing by David Stamp and Ken Wills)