Two children and another civilian were killed along with a soldier in firing across the border between India and Pakistan, officials from both sides said Monday, as tensions soar between the nuclear-armed rivals.

Pakistan's military said an 18-month-old girl and another civilian were killed on its side of the border in "unprovoked firing" by the Indian army.

"Due to Indian unprovoked firing last night a civilian, Muhammad Latif of village Janglora, and a minor Haniya, age one and a half, embraced shahadat (martyrdom) while seven civilians were injured," a military statement said.

The firing took place across the border between Indian-held Kashmir and Pakistan's Punjab province in the villages of Harpal, Pukhlian and Charwah, the statement said.

Indian police said the late night heavy exchange of firing occurred in its RS Pura sector, killing an Indian border security guard and a six-year-old boy.

The Border Security Force (BSF) soldier died after he received splinters from a mortar shell fired by Pakistan rangers, Danish Rana, inspector general of police for the area, told AFP.

"The boy and the BSF soldier died during the intense exchange of small arms fire and mortars throughout the night along the border," Rana said.

Six other civilians were also injured during the exchange, said another Indian police officer speaking on condition of anonymity.

Relations between the two countries have plummeted in recent months, with India blaming Pakistani militants for a raid on an army base in its part of disputed Kashmir in September that killed 19 soldiers.

India later said it launched "surgical strikes" across the border in Pakistan on militant targets, prompting fury from Pakistan which denied the raids took place.

Pakistani military said late Monday a strong protest was lodged with the United Nations Military Observers for India and Pakistan over the Indian firing.

Indian and Pakistani troops regularly exchange fire across their de-facto border in Kashmir, but rarely send ground troops over the line.

The overnight incident comes days after Indian border security forces said they shot dead seven Pakistani soldiers in retaliation for a ceasefire violation, with Pakistan refuting the claims.

Muslim-majority Kashmir has been divided between India and Pakistan, but claimed in full by both, since the two countries gained independence from Britain in 1947.

Since 1989 several rebel groups have been fighting Indian forces deployed in the region, seeking independence or a merger of the territory with Pakistan.

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