* Ukraine holds parliamentary election on Sunday
* Separatist-held areas of east Ukraine will shun election
* Some in east say new president speaking Russian is good sign
* Ending the conflict remains very difficult task
DONETSK/SLOVYANSK, Ukraine, July 17 (Reuters) - In one of his first acts as Ukrainian president, comedian-turned-politician Volodymyr Zelenskiy held out a symbolic olive branch to people in Ukraine's mostly Russian-speaking Donbass region, by switching from Ukrainian to Russian.
That gesture, during his inauguration in the Ukrainian parliament in May, sent a message of inclusion to people in the mainly separatist-controlled Donbass region. And for some, at least, it offers a faint glimmer of hope in a conflict that has claimed 13,000 lives and shows no sign of resolution.
Language was a factor in the outbreak of the conflict in 2014, with Russian speakers in Donbass saying they feared Kiev would impose the Ukrainian language on them. Ukraine says Russia exploited such fears to foment an anti-Kiev uprising that it also backed with troops and weapons. Moscow says it only provides political and humanitarian support to the rebels.
Separatist-controlled areas of the Donbass did not take part in Ukraine's presidential election in April, won by Zelenskiy, and will also shun Sunday's parliamentary poll, which the new president's Servant of the People is expected to win on an anti-corruption platform.
But for the Donbass, Zelenskiy has broken the mould of Ukrainian leaders who since 2014 - when Moscow also seized Ukraine's Crimea region - have avoided using Russian in public.
"He knows Russian better than Ukrainian, whatever they teach him over there. He won't ever know Ukrainian as well as Russian," Lyudmila Korneeva, 65, a market stall worker, told Reuters TV in Donetsk, the biggest city in the Donbass.
Dmitry Barabanov, 31, who runs a shisha bar in Donetsk, said Zelenskiy speaking both Ukrainian and Russian reflected the reality for people in the region.
"We border Russia. All of us have relatives in Russia, all of us got used to this language and speak Russian here," he said. "When I go to Ukraine, I speak Russian and Ukrainian."
Zelenskiy has said he will do everything in his power to end the conflict in Donbass, but without territorial concessions to the separatists.
Doing a deal in Donbass remains fraught with difficulty.
The separatists distrust Kiev, their Russian backers have given no sign they are willing to meet Kiev's demands, and a majority of Ukrainian voters might not forgive anything they see as compromising Ukraine's territorial integrity.
"Many people favour it (peace) at any price... For me that's absolutely unacceptable," said Alexei Pichakhchi, who moved from rebel-controlled Donetsk to Slovyansk, a city retaken by government forces during a major rebel retreat in 2014.
"I lived in Donetsk, had an amazing job, everything was good. And then this 'Russian world' came up and I simply couldn't live with it," he said, referring to the Russian nationalism of the separatists. "How can you talk about compromises with people who destroyed your life?" (Reporting by Sergei Kirichenko and Serhiy Takhmazov, writing by Maria Tsvetkova Editing by Gareth Jones)