India has conducted "surgical strikes" on suspected militants in Pakistan it suspects of preparing to infiltrate into the part of Kashmir it controls, the army's director general of military operations said on Thursday.

Lt General Ranbir Singh told reporters the strikes were launched on Wednesday based on "very specific and credible information that some terrorist units had positioned themselves to infiltrate".

Singh said the strikes had caused significant casualties, and that he had called his Pakistani counterpart to inform him of the operation.

An army source said that the strikes were launched across the Line of Control, or de facto border between the two countries.

However, Pakistan said India's claim of a "surgical strike" across the countries' de facto border was an illusion, saying that the incident was "cross-border fire".

"The notion of surgical strike linked to alleged terrorists' bases is an illusion being deliberately generated by India to create false effects," the military said in a statement.

It was released shortly after the senior Indian military officer said India had hit suspected militants preparing to infiltrate into Indian-administered Kashmir along the Pakistani side of the border.

Pakistan's military confirmed that two of its soldiers had been killed in the exchange of fire across the Line of Control, which serves as the de facto border.

The exchange of fire took place in the Bhimber, Hot Spring, Kel and Lipa sectors in Pakistan-administered Kashmir, and lasted about six hours, the Pakistani military's press wing said in a statement.

An Indian army officer said that there had been shelling from the Pakistani side of the border into the Nowgam district of Indian-administered Kashmir.

"Pakistan troops fired at Indian posts in Nowgam sector of North Kashmir at midnight. They also fired mortars. Army at the LoC fired back and intermittent firing is going on," the army officer said on condition of anonymity, referring to the Line of Control, or heavily militarised de facto border.

There were no casualties or damage reported on the Indian side of the LoC.

Both India and Pakistan claim Kashmir in full, but govern separate parts, and have fought three wars since independence from Britain in 1947, two of them over Kashmir.

Tension between the South Asian rivals has been high since an Indian crackdown on dissent in Kashmir following the killing by security forces of Burhan Wani, a young separatist leader, in July.

They rose even further when New Delhi blamed a September 18 attack on an Indian army camp in Indian-controlled Kashmir, which killed 18 soldiers, on Pakistan.

A senior Indian police officer said that the army had begun searching for possible infiltration of militants in the Nowgam area after Thursday's firing.

Indian Prime Minister Narendra Modi chaired a meeting of his cabinet committee on security after the Indian army accused Pakistan of breaching a 2003 ceasefire in Kashmir.  - Reuters