Authorities deployed tens of thousands of additional soldiers in the already highly militarised region for the elections, which are being held in four phases.
Voter turnout was low on Monday morning in Muslim-dominated areas of the Kashmir valley.
Armed police and soldiers guarded over 800 polling stations across the India-held Kashmir (IHK) area of the disputed region as government forces laid razor wire and erected steel barricades on roads.
A curfew was in effect in parts of the city of Srinagar to prevent anti-India protests.
Shops, businesses and most schools were closed as part of a strike called by Kashmiri leaders.
India says the polls are a vital grassroots exercise to boost development and address civic issues.
Kashmiri leaders and armed Kashmiris who challenge India’s sovereignty over Kashmir have called for a boycott, saying the polls are an illegitimate exercise under military occupation.
Nearly 1.7 million residents are registered as voters for the urban polls.
Village council elections will be held separately in November.
According to officials, 244 candidates have already been selected unopposed and there are no contestants for more than 170 out of a total of 1,145 council seats.
Kashmir’s main pro-India political parties such as the National Conference and Peoples Democratic Party are boycotting the polls, accusing New Delhi of fiddling with Kashmir’s special status in the Indian constitution.
Despite the boycott, suspected Kashmiri fighters fatally shot two activists of the National Conference and critically wounded another on Friday.
Some people withdrew from the elections after Kashmiri fighters threatened candidates and accused them of being “traitors and sellers of martyrs’ blood”.
Authorities have deployed more than 40,000 additional soldiers to guard the voting.
Anti-India sentiment runs deep in Kashmir’s mostly Muslim population and most people support the cause against Indian rule.
Nearly 70,000 people have been killed in the uprising and the ensuing Indian military crackdown.