At least 10 Indian and Pakistani soldiers and civilians have been killed in fighting over the past week. Two soldiers from the Border Security Force (BSF) have been killed in the last week.
About 6,000 civilians in Kashmir fled from their homes late on Monday as fighting moved to civilian areas, said Shantmanu, the divisional commissioner of Jammu region. About 4,000 left after fighting began last week.
"We had a narrow escape and there is a war-like situation," said Sham Kumar, 54, from Sherpur village. "Pakistani troops are using long-range weapons. It is the first time we have seen such intense shelling." Kumar said he left his village after a shell landed in a school about 3.5 km (2 miles) from the border.
The violence comes days before US Secretary of State John Kerry is due to visit India. President Barack Obama is also due to visit India later this month as the Chief Guest for the Republic Day celebrations.
Last week, Defence Minister Manohar Parrikar warned that India would retaliate with double the force if Pakistan violates the ceasefire, which was agreed upon in 2003.
In August, India called off talks with Pakistan after Islamabad insisted on consulting Kashmiri separatists ahead of the dialogue.
In October, nearly 20 civilians were killed in both countries as cross-border violence escalated to its worst in over a decade.