In many Muslim-dominated areas, however, turnout was so low that paramilitary soldiers and police outnumbered voters.
And in some towns, police and protesters against the polls clashed.
The elections are being held in seven phases until December 24 in a staggered process that allows the government to deploy thousands of security forces in each area in an attempt to prevent a repeat of violence during elections in 2002 in which dozens died.
Police said they feared more unrest, particularly from separatist groups, although separatists have vowed not to use violence to enforce the boycott and campaigning was mostly peaceful.
The elections come just weeks after some of the worst protests against Indian rule in the country's only Muslim state.
At least 48 people died in the demonstrations which were the largest pro-independence protests across Kashmir in two decades.
The protests prompted a crackdown on separatist leaders who oppose the polls.
More than 30 people who called for a boycott have been detained in recent days under legislation that allows police to hold people for up to two years without trial.
The detainees were held for advocating "secession, breach of the peace and intimidating people not to vote".
B Srinivas, a senior police official, said the police "will not allow anybody to campaign against the elections".
But Mirwaiz Umar Farooq, a key separatist leader who has been under house arrest for three days, said "you can't have free and fair elections in the presence of hundreds of thousands of occupying forces".
The final count for the state is expected on December 28.