The army said "significant casualties has been caused to these terrorists and those who are trying to support them".
Pakistan has denied any strikes were carried out by India across the border.
"The notion of surgical strike linked to alleged terrorists` bases is an illusion being deliberately generated by India to create false effects," the Pakistani military said in a statement.
Pakistan confirmed that two of its soldiers had been killed in an exchange of fire along the Line of Control that divides the disputed region. It said the Indian firing had been "unprovoked".
Tensions have been high since a militant attack on an Indian army base in Kashmir left 18 soldiers dead earlier this month. India blamed the attack on Pakistan, which denied the claim.
`Evil design`
India`s military gave few details of the operation it says it carried out overnight.
At a joint press briefing by the army and the foreign ministry, officials said the "motive of the operation was to hit out at terrorists who were planning to infiltrate into our territory".
India`s Director General of Military Operations, Lt Gen Ranbir Singh, also blamed Pakistan for "being unable to control terror activities in territories under its control".
The "surgical strikes" on alleged "terror launch pads" alongside the de-facto border had caused "significant damage to terrorists".
But there was no mention of where the strikes took place or any casualties.
Pakistani army officials said the fighting started in the early hours of the morning and continued for about six hours.
The country`s Prime Minister, Nawaz Sharif, criticised the "unprovoked and naked aggression of Indian forces" and said his military was capable of thwarting "any evil design to undermine the sovereignty of Pakistan".
The 18 September attack on the base at Uri in Indian-administered Kashmir was the deadliest of its kind for years.
Islamabad says India`s stance is a "blatant attempt" to deflect attention from human rights abuses in the region.
More than 80 people, nearly all anti-government protesters, have died in more than two months of violence against Indian rule.
Both India and Pakistan claim Muslim-majority Kashmir in its entirety but control only parts of it.
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