* Two dead in Kharkiv violence after one killed in Donetsk
* Kiev fears Moscow may exploit threat to ethnic Russians
* Moscow sees nationalist threat, says offering protection
* People in eastern Ukraine divided on their future (Adds new Russian foreign ministry comment)
By Alastair Macdonald and Lina Kushch
KIEV/DONETSK, March 15 (Reuters) - Ukraine accused "Kremlin agents" on Saturday of fomenting deadly violence in Russian-speaking cities and urged people not to rise to provocations its new leaders fear Moscow may use to justify a further invasion after its takeover of Crimea.
From his speaker's chair in parliament, acting president Oleksander Turchinov referred to three deaths in two days in Donetsk and Kharkiv and said there was "a real danger" of invasion by Russian troops across Ukraine's eastern border.
Using language similar to that which preceded the seizure of Crimea two weeks ago, Russia's foreign ministry issued a new statement on Saturday saying Moscow was considering "numerous appeals with requests for defence of peaceful citizens" after "provocations" by "ultra-nationalist militants".
Addressing members of the party of the Moscow-backed president ousted in last month's Kiev uprising, Turchinov said: "You know as well as we do who is organising mass protests in eastern Ukraine - it is Kremlin agents who are organising and funding them, who are causing people to be murdered."
Two men, described by police as pro-Russian demonstrators, were shot dead in a fight in Kharkiv late on Friday. A Ukrainian nationalist was stabbed to death when pro-Russia and pro-Ukraine demonstrators clashed in Donetsk on Thursday.
Other members of the Western-backed interim administration, which Russian President Vladimir Putin's government says includes "fascists" hostile to ethnic Russians, urged people in the east not to be drawn into violence stirred up by Moscow.
Russian forces occupied Crimea two weeks ago, triggering an ominous confrontation with Western powers, after Putin said he would protect Crimea's ethnic Russian majority and compatriots elsewhere in Ukraine. As Crimeans vote in a referendum on Sunday that could bring annexation by Moscow, Kiev fears Russia could widen the scope of its takeover by moving troops into the east.
The interior minister accused ousted president Viktor Yanukovich of promoting unrest with "extremist Russian forces". Arsen Avakov issued an appeal on Facebook: "Don't let them manipulate you!" he said. "This isn't a game of toy soldiers."
Two men, aged 21 and 30, were killed by buckshot late on Friday when pro-Russian demonstrators surrounded an office of the far-right Ukrainian nationalist group Right Sector, which rose to prominence fighting riot police in Kiev over the winter.
Police said 32 Right Sector activists and six pro-Russian demonstrators were detained and a number of weapons seized.
A spokesman for Right Sector in Kharkiv said his group had been besieged in their office overnight by pro-Russian activists firing shotguns and rifles and throwing petrol bombs and stun grenades. Avakov said both sides had used firearms.
Kharkiv governor Ihor Baluta said unidentified men in a minibus provoked a confrontation with pro-Russia demonstrators and then drove off. When pursuing demonstrators caught up with the vehicle, it was parked outside the nationalists' building.
The Right Sector spokesman, quoted by Interfax-Ukraine news agency, said his group had taken no part in the initial clash and believed the minibus was left outside its office by others.
The prominence of groups like Right Sector in positions of influence in Kiev, and measures such as a shortlived move last month to end the use of Russian as an official language, have been cited by Russia as grounds for its involvement in Ukraine.
Western powers, preparing economic sanctions against Russia over Crimea, largely dismiss Russia's characterisation of the new authorities in Kiev as the successors of Nazi-allied Ukrainian forces which fought the Red Army in World War Two.
Russian forces have been conducting large-scale exercises close to Ukraine's eastern frontier but Moscow's foreign minister said on Friday it had no plans to invade.
Authorities in Kharkiv banned political gatherings that were planned in the city over the weekend. In Donetsk, hundreds of people rallied in Lenin Square, flying Russian flags and calling for a referendum in the region similar to that in Crimea.
Some of the crowd later broke windows at the local security service office, seeking the release of a jailed former official.
Home to a million people, Donetsk is the heart of the Donbass coal and steel region that anchors Ukraine's industrial base. Many ethnic Russians live there as well as ethnic Ukrainians who use Russian as their first language.
Eastern Ukraine was part of the Russian empire for centuries, unlike western regions which came variously under Austrian and Polish rule. There, Ukrainian is widely spoken and support for closer ties to the European Union is strong.
People in Donetsk voice mixed feelings about the confrontation with Russia that has plunged Europe back toward the atmosphere of the Cold War of a quarter-century ago.
"I'm worried about Ukraine. I'm crying all the time," said Tatyana Lazunova, a physical education teacher in her 30s.
"I don't want to be under Russia."
Natalya Sedova, 50, said she was "for a united Ukraine and against occupation" and that, as an ethnic Russian, she felt no threat in Ukraine. She feared pro-Russian activism was part of efforts by corrupt allies of the ousted president to return. "All these Russian demonstrations are just pretend," she said.
But others in the city say political and economic turbulence in Ukraine is frightening and see Moscow as stable.
"We're already fed up with the Maidan," said 50-year-old mathematician Oleg Laktionov, using the name for Kiev's central square that stands for the protest movement against Yanukovich.
"Ukraine needs stability and calm. We won't get that in Ukraine, but in Russia I think we will," he said, adding that he wanted a referendum to decide whether Donetsk would gain autonomy within Ukraine, full independence or union with Russia.
He said military help from Russia to eastern separatists should be a last resort, however. "From Putin, we expect mainly diplomatic and political support," he said. "If the Nazis in Kiev put us under pressure, then we would like economic aid."
Student Dmitry Maksimenko said he too wanted a referendum on autonomy and expected Russian help. "If a single Russian gets hurt here, Putin won't hold back and will send in his troops."
Volodymyr Fesenko of the Penta think-tank in Kiev said a Russian takeover of eastern Ukraine would be more complex than Crimea, which is clearly defined geographically, was only given to Ukraine by Soviet rulers 60 years ago and already has an autonomous political structure and leaders favouring Russia.
The industrial "oligarchs" who dominate the east wanted neither to answer to Putin nor the break-up of Ukraine, as that would be "bad for business". But it was hard to predict whether, as in Crimea, an invasion would follow "appeals for help" from local Russian-speakers, Fesenko said. "It's 50-50." (Additional reporting by Pavel Polityuk in Kiev and Jason Bush in Moscow; Editing by Ron Popeski)