India says the two soldiers were killed during an incursion by Pakistani troops into Indian-administered Kashmir.
The Indian Army says the body of one of the soldiers had been beheaded.
It says says the soldiers died after a firefight erupted in disputed Kashmir on Tuesday, as a patrol moving in fog discovered Pakistani troops about 500 metres inside Indian territory.
Pakistan's high commissioner to New Delhi was summoned to India's Ministry of External Affairs on Wednesday where he was handed a formal complaint.
He was told that India expects a full investigation by Islamabad into the clash.
Mr Kurshid described the incident as "unacceptable" and says India's response will be "proportionate".
Pakistan denied its troops were involved in any attack in its first official reaction since its high commissioner was summoned.
A Pakistani senior official said Pakistan's director general of military operations had spoken to his Indian counterpart by telephone to deny that his troops were responsible.
"Pakistan rejected Indian army allegations of cross-line control firing by Pakistani troops and killing any Indian soldier," the official said in a statement.
"Indian authorities were informed that Pakistan has carried out ground verification and checked and found nothing of this sort happened as being alleged by India."
The official accused India of propaganda to divert attention from a raid on Sunday, when Islamabad said one Pakistani soldier was killed by Indian troops who raided a Pakistani post.