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* Letter dated Feb. 8 uses language similar to Obama's
* Trump welcomes Lithuanian independence from Russian gas (Updates with more from letter, details on conflict)
By Andrius Sytas
VILNIUS, Feb 10 (Reuters) - U.S. President Donald Trump has expressed support for an undivided Ukraine in a letter to Lithuania's president, using language similar to his predecessor Barack Obama that is likely to be welcomed by Kiev and NATO allies.
Baltic nations have been alarmed by Trump's description of NATO as obsolete and praise for Russian leader Vladimir Putin, but the Feb. 8 letter posted on the website of the U.S. embassy in Vilnius stuck to Washington's previous position.
"Your support for the sovereignty and territorial integrity of Ukraine, as well as your efforts to increase energy diversification, advance our shared goal to enhance European and regional security," Trump told Lithuanian President Dalia Grybauskaite.
Ukraine and the West accuse Russia of invading the country's industrial east in April 2014 and sponsoring separatist rebels to prevent Kiev establishing closer ties with Europe and the United States. Moscow denies military intervention.
The conflict has killed some 10,000 people and last week saw its biggest flare-up in more than a year, risking a fragile, two-year-old ceasefire.
Lithuania was annexed by the Soviet Union in the 1940s and regained independence only with the collapse of communism in the 1990s. Trump's letter was to congratulate the president on her country's Feb. 16 declaration of independence 99 years ago, after an earlier period of domination by Tsarist Russia.
It is one of the European Union's most vocal supporters of the economic sanctions imposed on Russia over the Ukraine crisis. Trump suggested in a pre-inauguration newspaper interview sanctions could be softened in return for Russian nuclear disarmament.
In his letter, Trump praised Lithuania for its plans to meet NATO guidelines by increasing defence spending to 2 percent of economic output. The president has called on Europe to pay more towards its security.
"Lithuania is a valued NATO ally that leads by example through your commitment to our shared defense, as evidenced by increasing your defense spending to achieve NATO's agreed benchmark," he wrote.
He also welcomed Lithuania's "efforts to increase energy diversification", in an apparent reference to relying less on Russian gas.
Lithuania, with U.S. support, opened a liquefied natural gas terminal in 2014 that dramatically reduced Baltic states' dependency on gas supplied by Russian monopoly Gazprom, removing a tool of political influence from Moscow. (Writing by Robin Emmott; editing by Andrew Roche)