Inspector general of the Indian border security forces, Rakesh Kumar, said Pakistani forces shelled the village of Arnia on Monday, about 3 kilometres inside India's border, killing five and wounding at least 25 civilians.
A Pakistani military statement said four civilians including two children were killed near Sialkot, bordering the Indian state of Punjab.
Military officials said Pakistan's army separately attacked 10 Indian army posts.
Another Indian officer, Lieutenant-Colonel Brijesh Panday, said the army later shot dead three Pakistani-based militants trying to cross into India further along the heavily militarised line of control.
The latest round of mortar and gunfire began on Friday when Pakistan's army said it responded to "unprovoked firing" from the Indian side.
Indian defence minister Arun Jaitley said the army would retaliate to the latest violence.
"Let everybody be assured that our armed forces, our paramilitary forces are fully ready and they are responding to each of these provocations," he said.
The attack coincided with Eid, celebrated by Muslims in both countries.
The violence will put more strain on ties between the nuclear-armed rivals, who called off planned top-level dialogue in September after Pakistan consulted Kashmiri Muslim separatists.
The cancellation dashed hopes for any progress on peace after the election of India's prime minister Narendra Modi.
Mr Modi surprised many observers by inviting Pakistani prime minister Nawaz Sharif to his inauguration in May.
But relations have soured since Mr Modi called off talks last month and they failed to meet on the sidelines of the United Nations General Assembly in New York.
The Himalayan region of Kashmir has been a bone of contention between India and Pakistan since they became independent in 1947.
They have fought three wars and came close to a fourth in 2001, with regular clashes along their de facto border.