India and Pakistan exchanged heavy artillery fire along their contested frontier on Wednesday after New Delhi launched deadly missile strikes on its arch-rival, in the worst violence between the nuclear-armed neighbours in two decades.

At least 43 deaths were reported, with Islamabad saying 31 civilians were killed by the Indian strikes and firing along the border, and New Delhi adding at least 12 dead from Pakistani shelling.

The fighting came two weeks after New Delhi blamed Islamabad for backing an attack on the Indian-run side of disputed Kashmir, which Pakistan denied.

The South Asian neighbours have fought multiple wars over the divided territory since they were carved out of the sub-continent after gaining independence from British rule in 1947.

The Indian army said "justice is served," reporting nine "terrorist camps" had been destroyed, with New Delhi adding that its actions "have been focused, measured and non-escalatory."

Pakistan Defence Minister Khawaja Muhammad Asif accused Indian Prime Minister Narendra Modi of launching the strikes to "shore up" his domestic popularity, adding that Islamabad "won't take long to settle the score."

Pakistan military spokesman Ahmed Sharif Chaudhry said five Indian jets had been downed across the border overnight.

An Indian senior security source, who asked not to be named, said three of its fighter jets had crashed on home territory.

The largest Indian strike was on an Islamic seminary near the Punjabi city of Bahawalpur, killing 13 people according to the Pakistan military.

A government health and education complex in Muridke, 30 kilometres from Lahore, was blown apart, along with a mosque in Muzaffarabad – the main city of Pakistan-administered Kashmir – killing its caretaker.

Four children were among those killed in Wednesday's attacks, according to the Pakistan military.

Pakistan also said a hydropower plant in Kashmir was targeted by India, damaging a dam structure, after India threatened to stop the flow of water on its side of the border.

Pakistan had earlier warned that tampering with the rivers that flow into its territory would be an "act of war."

India's Defence Minister Rajnath Singh said the overnight operation was New Delhi's "right to respond" following the attack on tourists in Pahalgam in Kashmir last month.

Pakistan had denied any involvement in the Pahalgam assault and called for an independent probe.

Prime Minister Shehbaz Sharif labelled India's strikes a "heinous act of aggression" that would "not go unpunished." (AFP)