Four people were injured in a clash between supporters of the ruling Congress party and the YSR Congress party in Kothapalli village of Nandyal mandal in Kurnool district.
The activists of the two parties also clashed at a few places in Kadapa district.
Men and women queued up since 7 a.m. to cast their votes in 5,903 gram panchayats in 22 districts.
According to State Election Commission, over 18,000 candidates are in the fray for sarpanch posts and 115,703 candidates for 49,729 ward members.
The polling will continue till 1 pm and the counting of votes will be taken up at 2 pm. Results for both sarpanch posts and ward members may be announced on Tuesday evening.
The elections were originally scheduled for 6,140 gram panchayats in the first phase but due to heavy rains and floods, polling in 237 panchayats in six districts was postponed. Polls in these panchayats will be held on July 31, in the third phase.
As many as 2,642 sarpanches have been declared unanimously elected. Congress, Telugu Desam Party and YSR Congress have all claimed that majority of these elected sarpanches belong to their party.
Andhra Pradesh has 21,592 gram panchayats, of which 21,491 are going to polls in three phases - July 23, 27 and 31.
The elections to the local bodies are being held after a gap of two years. The polls could not be held due to problems in providing reservations to various sections.
The Supreme Court in February had asked the government to conduct elections to urban local bodies and Panchayati Raj Institutions on the basis of the existing 60.5 percent quota to backward classes, Dalits and tribals.
The central government had stopped the release of statutory grants to the tune of Rs.2,600 crore to Panchayati Raj Institutions due to non-conduct of elections.