Turchinov, who succeeded overthrown pro-Moscow president Viktor Yanukovich in February, urged the population to accept “round table” talks on greater autonomy.
But he said the “terrorists” who have seized police and government buildings in the east could not be included.
The coalition government he runs with prime minister Arseniy Yatsenyuk says the poll in the Russian-speaking Donetsk and Luhansk regions today are illegal.
Crimea voted to leave Ukraine and was annexed by the Russian Federation in March in a move western nations say was against international law.
The latest vote – organised on a largely ad hoc basis with no clear control on authenticity of ballot papers or voter lists – could have serious consequences for Ukraine and relations between Moscow and the West. It risks turning isolated clashes into civil war.
Turchinov, from the pro-EU Fatherland party, said that secession from Ukraine “would be a step into the abyss for these regions”.
He added: “Those who stand for self-rule do not understand that it would mean complete destruction of the economy, social programmes and life in general for the majority of the population in these regions.”
The atmosphere in major cities across the region was tense, though there were no reports of fighting yesterday.
In the port city of Mariupol, where between seven and 20 people were killed in fierce fighting on Friday, rebels blocked the streets with barricades of tyres, rubbish containers and chairs.
Smoke was still coming from the partially burnt-out city administration building. There was no sign of any Ukrainian forces.
Barricades were manned by a handful of pro-Russians wearing motorcycle helmets, some armed with batons or clubs, though no gunmen were visible.
Video on the YouTube website showed an armoured car captured by rebels set on fire and ammunition exploding.
Throughout the city of Slaviansk – the most heavily defended separatist base – streets were barricaded with tyres, furniture, cars and scrap iron.
In the city of Donetsk, rebels released several members of the Red Cross whom they had held for seven hours, one having been beaten, a Red Cross official in Kiev said.
Western states have prepared to step up pressure on Russia, whom they accuse of engineering the crisis to destabilise Ukraine.
Russia denies direct involvement but voices support for insurgents it says are defending themselves against a “fascist” Ukrainian regime and its troops. The new coalition in Kiev is regarded as moderate by the West.
German chancellor Angela Merkel and French president Francois Hollande said that if the 25 May national elections failed to go ahead because of the rebellion, this would further unsettle the country.
In that case, they would be “ready to take further sanctions against Russia”.
Western countries are expected to announce new economic sanctions over Russian president Vladimir Putin’s actions over Ukraine.
The European Union has so far imposed asset freezes and visa bans on 48 Russians and Ukrainians over Moscow’s annexation of Crimea.
EU diplomats say new sanctions will for the first time target companies.
The national elections in two weeks’ time are seen in Kiev as a way of establishing a fully legitimate, universally elected government following president Yanukovich’s flight to Russia in February.