Police in both countries said troops exchanged fire for hours overnight, killing a Pakistani man and injuring at least 22 others. Earlier violence on Monday killed nine civilians.
Tens of thousands of villagers have fled their homes near the border for safety, officials said. Indian and Pakistani TV showed images of homes destroyed by mortars and pocked by bullets.
The violence is one of the worst violations of a 2003 ceasefire between India and Pakistan. While minor skirmishes have been somewhat common over the years, many were shocked that this week's fighting fell over the Muslim holiday of Eid al-Adha and left civilian casualties.
"They have turned our festivity into wailing," said Fazal Hussain, a resident of the Pakistani village of Harpal. "We are burying our relatives, rushing the injured to the hospital instead of celebrating Eid."
Pakistani police officer Mohammad Anwar said Indian mortar shells slammed into houses and fields, killing the owner of a house in Bhagiari village and injuring six others there.
"One shell fell on the roof of my cousin's house, pierced through to the ground and exploded," said the victim's relative, Latif Shaikh. "We had to run for safety in the dark and somehow managed to get behind the mosque in the village."
The violence occurred along parts of a 200-kilometer (125-mile) border between Pakistan's Punjab province and the Indian-controlled portion of Kashmir. Pakistan also controls part of Kashmir further north, but no violence was reported there overnight.
The two countries have fought two wars since 1947 over their competing claims to the Himalayan region.
In the Indian town of Arnia, a mortar slammed into a sweets shop, blowing a hole in the roof and injuring three people. "We were so scared," said the shop's owner, Rohit Saini.
Panicked civilians were fleeing the border area, officials said.
"The entire belt of villages and clusters of homes alongside the border is affected, and thousands of people are leaving their homes for safe places," Pakistani police officer Shams Uddin said.
On the Indian side, officials helped more than 20,000 residents of Arnia and thousands from other villages to evacuate Monday. By Tuesday morning, more than 10,000 people had signed in at Indian government shelters, according to regional administrator Shantmanu, who goes by one name. Thousands more were staying with relatives or friends, he said.
With the fighting most intense at night, some villagers were returning to their homes temporarily during the day to feed livestock and check on their belongings.
The U.N. Military Observers Group in India and Pakistan plans to visit affected areas along the border, the Pakistani military said Tuesday after lodging a protest with the group alleging that Indian troops had fired first.
"It is sad that the Indian government has not been able to restrain its forces despite strong diplomatic protest by Pakistan," said a statement from Pakistani Prime Minister Nawaz Sharif's national security adviser, Sartaj Aziz. "We call upon Indian government to immediately cease fire and shelling and help us preserve tranquility."
India also accused Pakistan of starting this week's skirmishes, saying it was trying to create a distraction to help separatist militants infiltrate into Indian-controlled Kashmir. Pakistan has repeatedly denied this.
Pakistan border guards "again resorted to unprovoked mortar shelling and heavy firing" on Indian border posts, Indian border guard spokesman Vinood Yadav said. On Monday, Indian troops killed three suspected militants it said were trying to infiltrate.
"Pakistan should stop cease-fire violations now," Home Minister Rajnath Singh said on Monday, according to the Press Trust of India news agency.
This week's violence followed several meetings between the commanders of the two countries' border forces aimed at calming tensions. A similar outburst of cross-border violence in August caused about 15,000 villagers to flee temporarily.
The U.S. government expressed concern. "We continue to encourage the governments of India and Pakistan to engage in further dialogue to address these issues," State Department spokeswoman Jen Psaki said in Washington on Monday.