An exit poll says the party headed by Ukrainian President Viktor Yanukovych has swept regional elections.

But the main opposition party, run by former Prime Minister Yulia Tymoshenko, calls the vote the dirtiest in the past 20 years and refuses to recognize results in three key provinces.

Sunday’s vote is a test of Mr. Yanukovych’s commitment to democracy after his first fraud—marred grab at the presidency sparked the Orange Revolution in 2004. Critics say Mr. Yanukovych is seeking to build an authoritarian state.

The exit poll, conducted by the Ukrainian arm of GfK, an international market research firm, said on Monday that Mr. Yanukovych’s Party of Regions received 36.2 percent of the vote in local councils. Ms. Tymoshenko’s party got 13.1 percent.

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