The attack is the first of its kind since the two countries went to war in 1971.
Indian air force jets carried out strikes on militant camps inside Pakistan on Tuesday, a government minister said.
“Air Force carried out aerial strike early morning today at terror camps across the Line of Control and completely destroyed it,” minister of state for agriculture Gajendra Singh Shekhawat said on Twitter.
Pakistan’s military said Indian aircraft had crossed into its territory in the disputed Kashmir region and “released a payload” after Pakistan scrambled its own jets.
Indian news has quoted a government source saying 12 fighter jets crossed into Pakistan and destroyed a militant training camp.
“Air Force carried out aerial strike early morning today at terror camps across the Line of Control and completely destroyed it”
Gajendra Singh Shekhawat, Indian minister of state for agriculture
The 12 Mirage jets are believed to have struck “a major terrorist camp” with 1,000kg of explosives, according to Indian air force sources.
Pakistan’s armed forces spokesman major-general Asif Ghafoor accused India of breaching the terms of the ceasefire in the region.
“Indian Air Force violated Line of Control,” he tweeted.
“Pakistan Air Force immediately scrambled. Indian aircrafts gone back.”
The Line of Control is based on lines established after the first war the two countries fought over Kashmir shortly after India gained independence from Britain in 1947.
While there are often exchanges of artillery and light weaponry over the border, this represents a major incursion in the territory.
These latest early morning raids come at a time of high tensions between the two neighbouring countries — which both have nuclear weapons.
Earlier this month, a suicide attack on a paramilitary convoy killed at least 40 Indian security personnel.
More than 300 separatist activists have been rounded up in recent days, triggering fears of a major response from the Indian government.
Doctors have been warned to cancel any holidays and stockpile medicines in the region.
There were no reports of casualties or damage in Tuesday’s raids.
Last year, a retired general warned Daily Star Online that India would destroy Pakistan and China in a nuclear war.