Hennadiy Kernes was reportedly shot in the back by unknown gunmen while out jogging, and is said to be undergoing emergency surgery in hospital.
Monday also saw pro-Russian separatists seize a local government building in Kostyantynivka in eastern Ukraine.
The US and EU are preparing to impose fresh sanctions against Russian individuals and companies.
Western nations accuse Moscow of supporting separatist gunmen who are occupying official buildings in cities across eastern Ukraine.
The separatists continue to hold seven Western military observers who were seized last week in the region.
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