Kentucky Secretary of State spokesman Bradford Queen says voter turnout has been slow since polls opened on a cool, rainy election day.
The top race on Tuesday's ballot for Democrats is the presidential primary between Hillary Clinton and Bernie Sanders. Republicans held a presidential caucus in March, which was won by Donald Trump. Other major races on the primary ballot include seats for U.S. House, U.S. Senate and the state House.
Queen said by late morning, there had been no major problems reported.
The Attorney General's Office said it had received 11 calls from eight counties by 10 a.m. A majority of the calls were procedural questions, but three were reports of electioneering and one reported possible vote buying.
Voters can cast ballots until 6 p.m. local time.