Some 1.7 million voters could take part in ballots seen as a key test of political stability more than four years after a 2001 peace accord between government troops and ethnic Albanian guerrillas.
Zoran Tanevski of the state electoral commission indicated that turn out may be quite low, though polls are to stay open until 19:00 local time.
Several minor incidents were recorded in the west of the former Yugoslav republic, said an interior ministry spokesman.
Sunday’s vote, which is monitored by hundreds of local and foreign observers, is a test of reforms drawn up after a 2001 insurgency by ethnic Albanian rebels to seek greater autonomy from majority Macedonian Slavs.
The Organisation for Security and Cooperation in Europe (OSCE) had strongly criticised the first round on March 13, citing serious irregularities including group voting, ballot stuffing, stolen ballots and intimidation.
Macedonia’s Supreme Court ordered a repeat of first-round voting in 33 polling stations across 10 municipalities, including in the capital, Skopje, and in the second-largest municipality, Tetovo.