(Adds diplomats working on statement, U.S. aid for Ukraine)
* Three separatists die in overnight shooting -Ukrainian minister
* Four-way talks convene in Geneva
* Diplomats said to be working on joint statement
* Putin says Ukraine authorities heading for "abyss"
By Aleksandar Vasovic and Alexei Anishchuk
MARIUPOL, Ukraine/MOSCOW, April 17 (Reuters) - Separatists attacked a Ukrainian national guard base overnight and Kiev said three of them were killed, the worst bloodshed yet in a 10-day pro-Russian uprising, accompanied by tough words from Vladimir Putin that overshadowed crisis talks.
Ukrainian, Russian and Western diplomats held an emergency meeting in Geneva, seeking to resolve a confrontation that has seen pro-Russian fighters seize swathes of Ukraine while Moscow masses tens of thousands of troops on the frontier.
The United States, Russia, Ukraine and the European Union were working on a joint statement on the crisis but had not reached agreement and talks were continuing, a Western official said.
Seeking to put pressure on Moscow, NATO announced it was sending naval ships to the Baltic. The United States, in a move to reassure allies, approved more non-lethal military support for Ukraine, including medical and welfare supplies.
The Russian president, who overturned decades of post-Cold War diplomacy last month by declaring Russia had a right to intervene in neighbouring countries and annexing Ukraine's Crimea region, accused the authorities in Kiev of plunging the country into an "abyss".
Kiev fears he will use any violence as a pretext to launch an invasion of Ukraine by Russian forces.
"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 in his annual televised question-and-answer session with the Russian public.
"I hope that they are able to realise what a pit, what an abyss the current authorities are in and dragging the country into," said Putin, who reserved the right to use military force while still saying he preferred dialogue.
In Kiev, Prime Minister Arseny Yatseniuk said he expected little from the Geneva meeting because "I don't trust the Russian side."
In Moscow, Russian shares and the rouble rose however as investors drew hope from the talks in Geneva, shrugging off Putin's remarks about his "right" to send troops to Ukraine.
Ukraine, which sees Moscow's hand behind separatist uprisings in the east, said it would impose stricter border controls on Russian men seeking to enter the country. Russia said it might retaliate.
At the Ukrainian national guard headquarters in Mariupol, on the Sea of Azov, there was clear evidence the building had come under attack.
A grey police jeep was inside the compound on Thursday morning with broken windows, flat tyres and bent doors. The gates of the compound had been flattened. There were shell casings outside the gates and several unused petrol bombs.
"They came here around 8:15 p.m., demanding that we surrender our weapons and join the people. There were some women with them, but then they left," said police Major Oleksandr Kolesnichenko, deputy commander of the base.
"Then they used a truck to break through the gate. There was some incoming fire. I could not see who was shooting - it was dark," he said. "We fired first in the air. We fired warning shots after they entered the compound. We had no casualties."
A separatist representative, who gave his name only as Sergei, said there had been a peaceful rally at the base.
"We had a peaceful rally to urge the police to join the people. The commander of the compound warned he would order troops to shoot to kill."
"Then there was shooting. Some people came with Molotov cocktails. We have verified that one person is dead and more than 10 wounded."
Interior Minister Arsen Avakov said an armed group of about 300 separatists attacked the base with guns and petrol bombs. Three separatists were killed and 13 wounded, he said. No guardsmen were hurt.
The clash took place hours after a modest Ukrainian military operation to recapture territory elsewhere from armed pro-Russian rebels ended in disarray on Wednesday, with troops surrendering rather than open fire.
Putin's televised chat, in a talk show format with satellite link-ups with applauding audiences across Russia, lasted for several hours. His words were clearly directed both at a domestic audience and at a world still grappling with the implications of his new doctrine, which the West says dispenses with customary limits on the use of armed force.
The first questions were patched through from newly annexed 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.
A self-confident Putin pointed to authorisation he secured in March from the mostly appointed upper house of parliament to use force in Ukraine, though he said he preferred negotiations.
"The Federation Council granted the president the right to use military force in Ukraine. 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," Putin said.
"We must do everything to help these people (in eastern Ukraine) defend their rights and independently determine their own destiny."
He also hinted at wider territorial ambitions, saying the people of Transdniestria, a pro-Russian separatist enclave in another ex-Soviet Republic, Moldova, should also be permitted to "determine their own destiny".
Putin cast the Crimea annexation in explicitly geo-political terms, saying it was a response to the prospect that NATO could one day incorporate Ukraine and cut off Russia's access to its Black Sea Fleet. Previously the operation had been justified solely as reflecting the will of Crimea's residents.
He also acknowledged for the first time that Russian troops had played a direct role in Crimea, assisting local militia.
Putin's chat even featured a cameo appearance from Edward Snowden, the former U.S. security contractor given asylum in Russia after leaking information about surveillance by U.S. and British spy agencies. Snowden, patched in by video link, asked a question about Russian surveillance. Putin denied that Moscow carried out mass collection of citizens' data.
Pro-Russian militants control buildings in about 10 towns in eastern Ukraine after launching their uprising on April 6. In the biggest province in the region they have declared an independent "People's Republic of Donetsk".
On Wednesday, an armoured column of Ukrainian paratroopers was humiliated in an attempt to retake some towns. Pro-Moscow separatists took control of some of their armoured vehicles and crowds surrounded another column, forcing the troops to hand over parts of their rifles and retreat.
Acting President Oleksander Turchinov said on Thursday the entire paratrooper brigade would now be disbanded and those who surrendered would be punished.
So far, diplomacy has failed to keep up with events on the ground, with Russia's supporters seizing control of territory before Western countries can formulate a response.
The United States and European Union have so far imposed visa bans and asset freezes on a small number of Russian individuals, a response that Moscow has openly mocked. However, the Western states say they are now contemplating measures that could hurt Russia's economy more broadly.
Kiev and the West believe Russian agents are directing the insurgency, an accusation Putin dismissed as "rubbish".
Russian Defence Minister Sergei Shoigu, repeating longstanding denials Moscow's agents were operating in Ukraine, nevertheless implied they might be there after all.
"As for allegations of the use of Russian special forces in Ukraine, all I can say is: it's hard to look for a black cat in a dark room. Especially if it's not there. It's especially silly if the cat is clever, brave and polite." (Additional reporting by Richard Balmforth in Kiev, Stephanie Nebehay, Arshad Mohammed and Catherine Koppel in Geneva, Christian Lowe and Alexei Anishchuk in Moscow and Jeff Mason in Washington; Writing by Peter Graff; Editing by Will Waterman and Giles Elgood)