The polling began at 8 am in 2,773 polling stations, including 918 in Kashmir division and 1,855 in Jammu division, officials said.
The voting would end at 2 pm, they said.
The officials said 727 polling stations have been categorised as hypersensitive, including 493 in Kashmir division and 234 in Jammu division, for the third phase.
They said 5,239 candidates are in the fray for 358 sarpanch and 1,652 panch seats.
Ninety six sarpanchs and 1,437 panchs have been elected unopposed in this phase, they added.
The officials said an electorate of 4,23,592 are eligible for voting for sarpanch constituencies while 2,70,668 for panch constituencies.
They said all arrangements, including security related, have been put in place for smooth conduct of the polls.
The nine-phased elections, being conducted on the non-party basis, began on November 17.
In the first phase of the polls, 74.1 per cent polling was recorded across J-K, including 64.5 per cent in Kashmir division and 79.4 per cent in Jammu division.
In the second phase held on November 20, overall 71.1 per cent polling was witnessed across the state with 80.4 per cent in Jammu division and 52.2 per cent in Kashmir division.