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SLAVIANSK/LUHANSK Ukraine — Pro-Russian separatists poured scorn on peace overtures from Ukraine's new president Petro Poroshenko on Saturday as fighting rumbled on in the east of the country.

Taking the oath of office in Kiev, Poroshenko appealed to the rebels to lay down their arms, offering peaceful dialogue and immunity from prosecution to "those who don't have blood on their hands".

But rebel spokesmen in the self-styled Donetsk People's Republic, which has declared independence from Ukraine and wants to unite with neighboring Russia, told Reuters the fight would continue.

"What they really want is one-sided disarmament and for us to surrender. That will never happen," said a top separatist official, Fyodor Berezin. "As long as Ukrainian troops are on our soil, I can see that all Poroshenko wants is subjugation," he said by telephone from Donetsk.

A pro-Russian rebel holds a knife as he stands near a local government building in downtown Kramatorsk Saturday. The separatists are scorning peace overtures made by Ukraine's new president Petro Poroshenko, as fighting rumbled on in the east of the country.GLEB GARANICH / Reuters

Since Poroshenko's election on May 25, government forces have stepped up what they call an 'anti-terrorist' campaign against the Russian-speaking separatists in the east.

The rebels have fought back, turning parts of the east into a war zone. On Friday they shot down a Ukrainian army plane and killed a member of the interior ministry's special forces in the separatist stronghold of Slaviansk.

Fighting continued around Slaviansk on Saturday and smoke could be seen rising above the surrounding forests.

Ukrainian armored personnel carriers and military transport vehicles lined the road leading into the city, and soldiers behind concrete blocks and sand bags trained their machine guns on cars and buses driving out.

Inna, 38, was leaving by foot with her mother and grandmother, carrying bags with food, water and clothes.

"All you hear is shelling and bombing. Yesterday entire houses burnt down. We've been hiding in the cellar for three days and we finally decided to leave. There is no water or electricity," she said.

An armed pro-Russian separatist speaks with people in a car at a border post abandoned by Ukrainian guards at Chervonopartyzansk, near the Ukraine-Russia border on Saturday.SHAMIL ZHUMATOV / Reuters

In his speech, Poroshenko said the government was prepared to talk to peaceful citizens — "clearly not with gunmen and other scoundrels" — and would offer a safe corridor for fighters who had crossed the border from Russia to go home.

But his appeal appeared to fall on deaf ears.

"We have reached the point of no return," said Andrei Sukhanov, commander of the separatist Kaskad (Cascade) militia, manning a road block in Slaviansk.

— Reuters