According to survivors, 22 villagers were lined up and gunned down in the village of Thawa overnight.
The bullet-riddled bodies of 12 other people, who were kidnapped from another village on Sunday, were also found by police overnight into today.
There has been no immediate claim of responsibility.
The attacks occurred ahead of scheduled talks in New Delhi later this week between Indian Prime Minister Manmohan Singh and Kashmiri separatist groups.
In New Delhi today, senior Interior Ministry official Sri Prakash Jaiswal strongly condemned the violence. But he said the attacks will not halt peace efforts:
"I want to tell the people of Jammu and Kashmir not to worry, I want to tell the nation that do not be perturbed. Such incidents will not stop the country and especially Jammu and Kashmir from moving towards peace."
India and Pakistan each claim all of Kashmir, which remains divided. More than 40,000 people have been killed since an Islamic insurgency began in 1989 aimed at ending Indian rule in part of the province.