(Adds statements from NATO and Donetsk administration)
* Kiev says security operation underway in city of Slaviansk
* One officer killed, one also reported dead on rebel side
* Fears that confrontation could touch off wider violence
* NATO alarmed by well organised and armed men
* Russia warns Kiev not to use force against militants
By Thomas Grove
SLAVIANSK, Ukraine, April 13 (Reuters) - Ukrainian security forces launched an operation on Sunday to clear pro-Russian separatists from state buildings in the eastern city of Slaviansk, with dead reported on both sides as Kiev combats what it calls an act of aggression by Moscow.
With East-West relations in crisis, NATO described the appearance in eastern Ukraine of men with specialised Russian weapons and identical uniforms without insignia - as previously worn by Moscow's troops when they seized Crimea - as a "grave development".
Ukraine faces a rash of rebellions in the east that it says are inspired and directed by the Kremlin. But action to dislodge the armed militants risks tipping the stand-off into a new, dangerous phase as Moscow has warned it will protect the region's Russian-speakers if they come under attack.
One Ukrainian state security officer was killed and five wounded on the government side in what interior minister Arsen Avakov called Sunday's "anti-terrorist" operation.
"There were dead and wounded on both sides," Avakov said on his Facebook page, adding that about 1,000 people were supporting the separatists.
The Russian news agency RIA reported that one pro-Moscow activist was killed in Slaviansk in clashes with forces loyal to the Kiev government. "On our side, another two were injured," RIA quoted pro-Russian militant Nikolai Solntsev as adding.
The separatists are holed up in the local headquarters of the police and of the state security service, while others have erected road blocks around Slaviansk, which lies about 150 km (90 miles) from the Russian border.
However, details of the fighting remain sketchy. A statement from the administration of the eastern Donetsk region indicated the security officer may have been killed between Slaviansk and the nearby town of Artemivsk. Putting the number of wounded at nine, it said "an armed confrontation" was going on in the area.
Kiev accuses Moscow of trying to deepen violence and chaos in Ukraine, a former Soviet republic it once ruled. The Kremlin, it says, wants to undermine the legitimacy of presidential elections on May 25 which aim to set the country back onto a normal path after months of turmoil.
However, Russian Foreign Minister Sergei Lavrov said Kiev was "demonstrating its inability to take responsibility for the fate of the country" and warned that any use of force against Russian speakers "would undermine the potential for cooperation", including talks due to be held on Thursday between Russia, Ukraine, the United States and the European Union.
WELL ORGANISED ATTACKERS
Relations between Russia and the West are at their worst since the Cold War due to the crisis that began when Moscow-backed Ukrainian president Viktor Yanukovich was pushed out by popular protests in February.
Moscow then annexed Crimea from Ukraine, saying the Russian population there was under threat. Some Western governments believe the Kremlin is preparing a similar scenario for eastern Ukraine, something Moscow has strenuously denied.
In Kramatorsk, about 15 km south of Slaviansk, gunmen seized the police headquarters after a shootout with police, a Reuters witness said.
The attackers were a well-organised unit of over 20 men, wearing matching military fatigues and carrying automatic weapons, who had arrived by bus. Video footage showed the men taking orders from a commander. Their identity was unclear.
Their level of discipline and equipment was in contrast to the groups who have occupied buildings so far in Ukraine. They have been mostly civilians formed into informal militias with mismatched uniforms.
NATO Secretary-General Anders Fogh Rasmussen expressed concern about similarities in some of the separatists' appearance to that of the Russian troops who seized control in Crimea.
Calling on Russia to pull back its large number of troops, including special forces, from the area around Ukraine's border, he said in a statement: "Any further Russian military interference, under any pretext, will only deepen Russia's international isolation."
Moscow says the troops are on normal manoeuvres.
Lavrov said it was Ukraine's Western-leaning government, viewed by the Kremlin as illegitimate, that was stoking the tensions.
United Nations Secretary-General Ban Ki-moon said he was deeply concerned about the deteriorating situation in eastern Ukraine and "the growing potential for violent clashes".
GAS WAR RISK
The crisis over Ukraine could trigger a "gas war", disrupting supplies of Russian natural gas to customers across Europe. Moscow has said it may be forced to sever deliveries to Ukraine - the transit route for much of Europe's gas - unless Kiev settles its debts.
For now, though, the focus of the crisis was in eastern Ukraine, the country's industrial heartland, where many people feel a close affinity with neighbouring Russia.
In the eastern city of Kharkiv, several people were injured in clashes between supporters of the revolution that brought the Kiev leadership to power and opponents who favour closer ties with Russia. In another eastern town Zaporizhzhya Interfax news agency said 3,000 pro-European supporters turned out in a unity rally and faced off with several hundred pro-Moscow supporters, many of them waving the Russian flag.
"We are ready to defend ourselves," said separatist Vyacheslav Ponomaryov, who said he had taken over leadership of Slaviansk after the city's mayor fled.
Yulia Tymoshenko - a former Ukrainian prime minister who was jailed under Yanukovich and is running for next month's presidential election - said the unrest in eastern Ukraine was the work of Russian state security agents, designed to wrongfoot the EU and United States, which have imposed sanctions over the Crimean annexation, at Thursday's talks in Switzerland.
"There is an ulterior motive for this aggression, because in a few days there will be big negotiations in Geneva which Russia, out of weakness because of financial sanctions, asked for," she was quoted as saying by Interfax news agency. (Additional reporting by Conor Humphries and Natalia Zinets and Richard Balmforth in Kiev, Alessandra Prentice in Moscow and Adrian Croft in Brussels; Writing by Christian Lowe, David Stamp and Will Waterman)