In a telephone conversation with Secretary-General Ban Ki Moon, Turchynov suggested that an "anti-terrorist operation" could be conducted jointly by Ukrainian security forces and UN peacekeepers, according to the presidential web site.
Peacekeepers would have to be authorised by the UN Security Council, in which Russia holds a veto.
The request comes from a government that has proved powerless to reign in separatists in the Russian-speaking east of the country, where insurgents have been occupying government offices in cities for the past week.
Instead, violence continued. A pro-Russian mob stormed a police station in yet another city near the Russian border, while gun men took control over a military airport in the ear. The Kiev government and Western officials accuse Russia of instigating the unrest and of deploying armed Russian agents to carry them out.
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During the storming of a police station in the city of Horlivka earlier today, one man identified himself as a lieutenant colonel of the Russian army.
Later in the day, armed men in masks also seized control of a military airport outside the city Slovyansk, also in the Donetsk region.
The developments came as European Union foreign ministers met in Luxembourg to consider further sanctions against Russia, and three days ahead of a scheduled conference in Geneva involving diplomats from the United States, Russia, the European Union, Ukraine and Switzerland, which is intended to seek ways of defusing tensions.