Ukraine's interim President Oleksandr Turchynov, who is also Parliament Speaker. Photo by EPA/BGNES.

Ukrainian interim President Oleksandr Turchynov has said Kiev will grant amnesty to to pro-Russian activist in two eastern cities if they choose to hand over their weapons.

Turchynov has vowed to sign a presidential order to free them of future charges if they leave the buildings they have taken over.

The acting President thus repeated the idea put forward by an amnesty bill which MPs from former head of state Viktor Yanukovych's Party of Regions introduced in Parliament on Wednesday, Russia's Lenta.ru reports.

The country earlier issued an ultimatum to protesters, with a deadline to leave seized buildings due to end on Friday.

On Tuesday, an "anti-terrorist" operation was kicked off to end what the government calls "separatist action", after Donetsk was proclaimed "People's Republic" by demonstrators.

Pro-Russian activists have been occupying administration buildings in the cities of Donetsk and Luhansk to the east of Ukraine for the last few days.

The government in Kiev says Russia is behind their actions as it is looking for a pretext to invade Ukraine, something which Moscow has denied.

Eastern parts of the country are populated by a Russian-speaking (though not describing itself as "ethnic Russian") majority, and mass protests in some main cities have recently raised fears the region could follow Crimea's example and incorporate itself into the Russian Federation.

The EU, US, Russia and Ukraine are to discuss thr situation in a four-way meeting next week.

The KyivPost has quoted the spokeswoman for EU's foregn policy chief Catherine Ashton as saying that the forthcoming talks are envisaged to be at a Foreign Minister level.

Meanwhile, the Parliamentary Assembly of the Council of Europe condemned Russia's annexation of Crimea in a resolution.