He said the deaths of two Indian soldiers - one of whom India says was beheaded - were "unacceptable".
His remarks follow the Indian army chief's call form troops to "aggressively" respond to firing from Pakistani troops.
Both countries claim Kashmir and have fought two wars over it.
Two Pakistani soldiers were also killed last week.
The violence has plunged the neighbours into the worst crisis in relations since the Mumbai attacks of 2008, which were blamed on militants based in Pakistan. Both sides deny provoking last week's clashes.
Claimed by both countries, Kashmir has been a flashpoint for over 60 years. Exchanges in the disputed area are not uncommon but rarely result in fatalities.
The prime minister made his remarks in the capital, Delhi, to mark Army Day.
"After this barbaric act, there cannot be business as usual with Pakistan. What happened at LoC is unacceptable," he said, referring to the Line of Control, which divides Kashmir.
"I hope Pakistan realises this. I hope Pakistan will bring the perpetrators to book."
India was set to begin a landmark visa-on-arrival deal for Pakistani seniors at the Wagah crossing, but this has been put on hold.Officials from both countries held a meeting at the border on Monday aimed at reducing tensions. Neither side have commented on the talks.
Both countries have also summoned each other's envoys to protest about the killings of the soldiers. Pakistan denies Indian accounts of what happened.
The Indian army chief, Gen Bikram Singh, on Monday accused Pakistan of planning the attacks that killed the two Indian soldiers.
He said the 8 January attack was "pre-meditated, pre-planned activity" and urged Indian troops to be "aggressive and offensive in the face of provocation and fire" from Pakistan.
The border clash has come as a major setback to ties between the two neighbours, with the prime minister saying Pakistan was living in denial, says the BBC's Sanjoy Majumder in Delhi.
In a related development, eight Pakistani hockey players who were due to take part in a tournament in India are being sent back, our correspondent adds.
India suspended a peace process with Pakistan following attacks by Pakistan-based militants in Mumbai in 2008. Negotiations resumed in February last year.
Thousands of people have been killed in Indian-administered Kashmir since an armed revolt against Indian rule erupted in 1989. There has been a ceasefire in Kashmir since late 2003.