(Combines earlier stories, adds background)
* Putin denounces Kiev's use of military in east Ukraine
* Does not rule out sending in Russian troops
* Kiev leadership 'dragging country into abyss'
* Geneva talks important, 'mutual understanding' possible
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 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 that was 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.
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."
He said crisis talks taking place in Geneva on Thursday were very important, and urged the government in Kiev to sit down to negotiate with the Russian-speaking communities in the east of the country.
"The start of today's talks are very important, because it is important that we together think about how to get out of the situation," Putin said, referring to the Geneva meeting between Russia, Ukraine, the United States and the European Union.
In a later 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."
After popular protests forced Ukraine's pro-Moscow president to flee in February, Russia asserted its right to intervene in its neighbour to protect the rights of ethnic Russians. Last month it annexed the Ukrainian Black Sea peninsula of Crimea.
By massing tens of thousands of troops on the Ukrainian border, it has prompted fears in Kiev and the West that it might go further by invading the Russian-speaking east of the country.
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 Putin 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.
He said Kiev needed to provide guarantees to its Russian-speaking population in the east of the country to resolve the crisis.
"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 John Stonestreet)