Thais voted nationwide on Sunday in provincial elections that mark the first test of democracy since a general election last year that drew accusations of manipulation and helped spawn months of youth protests.

The elections in Thailand’s 76 provinces outside the capital Bangkok are the first since Prime Minister Prayuth Chan-ocha, who kept power after last year’s ballot, overthrew an elected government in a military coup.

“It’s my duty to vote,” said 27-year-old bank worker Korkiet Akaraparn, voting in...