Indian and Pakistani soldiers exchanged gunfire overnight in Kashmir, a day after the worst violence between the nuclear-armed rivals in two decades.

Pakistani Prime Minister Shehbaz Sharif pledged to retaliate after India launched deadly missile attacks on Wednesday morning, with days of repeated gunfire along their border escalating into artillery shelling.

“We will avenge each drop of the blood of these martyrs,” Sharif said, in an address to the nation.

India said it had destroyed nine “terrorist camps” in Pakistan in “focused, measured and non-escalatory” strikes, two weeks after New Delhi blamed Islamabad for backing an attack on tourists in the Indian-administered side of disputed Kashmir – a charge Pakistan denies.

At least 44 deaths have been reported from both sides of the border following Wednesday’s violence, including children. Islamabad said 31 civilians were killed by Indian attacks and firing along the border. New Delhi said 13 civilians and a soldier had been killed by Pakistani fire.

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

Madasar Choudhary, 29, described to the AFP news agency how his sister saw two children killed in Poonch, on the Indian side of the frontier, on Wednesday.

“She saw two children running out of her neighbour’s house and screamed for them to get back inside,” Choudhary said, narrating her account because she was too shocked to speak. “But shrapnel got to the children – and they eventually died.”

Muhammad Riaz said he and his family had been made homeless after Indian attacks hit Muzaffarabad, the main city of Pakistan-administered Kashmir.

“We have no place to live,” he told AFP. There is no space at our relatives’ house. We are very upset; we have nowhere to go.”

On Wednesday night, Pakistan military spokesman Ahmed Sharif Chaudhry reported firing across the Line of Control – the de facto border in Kashmir – and said the army had been authorised to “respond in self-defence” at a “time, place and manner of its choosing”.

India’s army on Thursday morning reported firing “small arms and artillery guns” in multiple sites overnight, adding that its soldiers had “responded proportionately”, without giving further details.

India and Pakistan have fought multiple times since the violent end of British rule in 1947, when colonial officers drew straight-line borders on maps to partition the nations, dividing communities.

Muslim-majority Kashmir – claimed by both India and Pakistan – has been a repeated flashpoint.