* Putin denounces Kiev's use of military in east Ukraine
* Does not rule out sending in Russian troops
* Reminds Europe of dependence on Russian gas
* Geneva talks important, "mutual understanding" possible
* First questions come from grateful crowd in Crimea (Adds comments on Ukrainian election, gas exports, Moldovan region)
By Alissa de Carbonnel and Alexei Anishchuk
MOSCOW, April 17 (Reuters) - Russian President Vladimir Putin accused Ukraine's leaders on Thursday of committing a "grave crime" by using the army to try to quell unrest in the east of the country, and did not rule out sending in Russian troops.
But, addressing Russians in his annual televised phone-in, Putin said he hoped he would not need to take such a step, and that diplomacy could succeed in resolving the standoff.
In a marathon session dominated by questions on Ukraine, Putin tempered withering criticism of the Ukrainian leadership with more conciliatory comments about the possibility of a compromise to resolve the worst East-West crisis since the Cold War.
He pointedly reminded Europe of its dependence on Russian gas, and defended Russia's annexation of Crimea as, in part, a response to NATO's eastward expansion.
While recalling that parliament had granted him the right to use military force in Ukraine, the Kremlin chief said: "I really hope that I do not have to exercise this right and that we are able to solve all today's pressing issues via political and diplomatic means."
Ukraine sent in troops this week to try to recapture a series of eastern towns from pro-Russian militants, but their first attempt on Wednesday ended in disarray, with some armoured troop carriers retreating and others falling into the hands of the separatists.
"Instead of realising that there is something wrong with the Ukrainian government and attempting dialogue, they made more threats of force ... this is another very grave crime by Kiev's current leaders," Putin said.
"I hope that they are able to realise what a pit, what an abyss the current authorities are in and dragging the country into."
Russia refuses to recognise the Ukrainian leadership that took power in February after mass protests forced Viktor Yanukovich - the elected, pro-Moscow president - to flee.
Putin said the campaign to elect a new Ukrainian president next month was being conducted "in an absolutely unacceptable way", with some candidates being beaten up.
"If everything continues in this way, then of course we cannot recognise as legitimate what is happening and what will happen after May 25," he said, referring to the date of the vote.
But in more emollient comments, he stressed the importance of crisis talks taking place in Geneva on Thursday between Russia, Ukraine, the United States and the European Union.
In another answer, he added: "I'm sure we will come to a mutual understanding with Ukraine. We will not be able to do without each other."
Since the toppling of Yanukovich, Russia has asserted its right to intervene in its neighbour to protect the rights of ethnic Russians. Last month it annexed Crimea, a southern peninsula of Ukraine, after residents voted to break away from Kiev in a referendum deemed illegal by the West.
By massing tens of thousands of troops on the Ukrainian border, Moscow has prompted fears in Kiev and the West that it might go further by invading the Russian-speaking east of the country, even though Putin said that was not his intention.
The crisis has alarmed Russia's neighbours, which fear it may not stop at Crimea and may seek to grab back further chunks of former Soviet territory.
In comments likely to heighten such concerns, Putin said the the people of Transdniestria - a breakaway, Slav-dominated region of ex-Soviet Moldova - should have the right to decide their own fate, though he stressed the need for negotiations.
"People should be allowed to determine their own destiny. That's what we will work on with our partners," he said.
The United States and the European Union have imposed visa bans and asset freezes on dozens of Russians in retaliation for the annexation of Crimea, but so far avoided wider sanctions that could hurt their own companies as well as Russia's.
Alluding to that dilemma, Putin cast doubt on whether Europe could end its dependence on Russian gas.
"We sell gas in European countries which have around 30-35 percent of their gas balance covered by supplies from Russia. Can they stop buying Russian gas? In my opinion it is impossible," he said.
At the start of the phone-in, Putin fielded questions from Crimea, where hundreds of sailors, veterans and members of the public were lined up on the sea front in Sevastopol, headquarters of Russia's Black Sea fleet.
One questioner was interrupted by chants of "Thank you, thank you" as members of the crowd, many waving the Russian tricolour, expressed their gratitude to the Kremlin leader for absorbing Crimea into Russia.
While Putin was speaking, Ukraine's state security force said it had detained about 10 Russian citizens with intelligence backgrounds.
But Putin said Ukrainian assertions that Russian forces were present in east Ukraine were "rubbish".
"It's all nonsense. There are no kinds of Russian units in eastern Ukraine. No special forces, no instructors. They are all local citizens," he said.
Putin accused the Ukrainian leadership of talking only to its own appointees in the troubled eastern regions instead of opening what he called a genuine dialogue with the people.
"The compromise must be found not between third party players but between the different political forces within Ukraine itself," Putin said. "This is extremely important, it is the key issue." (Writing by Mark Trevelyan; Editing by Louise Ireland)