NATO launched a pair of artillery strikes across the border into Pakistan after attackers hiding there fired a barrage of rockets into Afghanistan that killed three children, officials said Sunday.

The cross-border fighting could heighten diplomatic tension over Pakistan's inability to stop Islamic militants from operating from its territory — and whether forces in Afghanistan have the right to strike back.

NATO said five rockets were fired at one of its bases in Khost province overnight. At least one hit a house in Kunday, a small village that sits between two military bases, killing the three children. Another hit a NATO base, wounding an Afghan man, the alliance said.

An Associated Press reporter saw the bodies of two of the slain children before relatives carried the three caskets, draped in colorful cloths, to a graveyard for burial Sunday morning.

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NATO said its forces responded "in self-defense" to the attack "with artillery fire on the launch site located about 300 meters (yards) inside Pakistan."

In an earlier attack Saturday afternoon, three rounds of "indirect fire" — which often refers to mortar or rocket attacks — landed near a NATO outpost in neighboring Paktika province, the alliance said. Three more landed in an Afghan army compound. No casualties were reported.

NATO said those rounds also came from inside Pakistan and responded with artillery fire.

Pakistan's military was notified immediately after each of the attacks, it said.

Afghan and U.S. officials blame surging violence in Afghanistan in part on efforts by the new Pakistani government to make peace with militants on its side of the mountainous frontier.

Last year, more than 8,000 people were killed in insurgency-related attacks — the most since the 2001 U.S.-led invasion — and violence has claimed more than 1,700 lives so far this year.

Pakistan's army has pulled back some forces from its lawless tribal areas, where al-Qaida and the Taliban find refuge, and has largely held fire during the peace talks — a pause critics say has allowed insurgents to intensify strikes into Afghanistan.

Cross-border military relations were further strained when U.S. warplanes apparently bombed a Pakistani border post in the Mohmand tribal region earlier this month, killing 11 Pakistani troops.

Secretary of State Condoleezza Rice has expressed regret over the incident, which the Pakistan army described as "cowardly." However, it remains unclear why the Pakistani post was struck.

Pakistan's army spokesman was not immediately available for comment Sunday. Another Pakistani military official, who is not authorized to speak on the record, said the NATO rounds fired in the earlier incident landed far from the nearest Pakistani border post.

NATO reported that another overnight barrage of rockets aimed at a base in Khost — this time from inside Afghanistan — killed another civilian. It responded with an airstrike as well as artillery fire, it said.

There was no word on any militant casualties.