ISLAMABAD - Pakistan on Monday denied accusations by Afghanistan that it fired hundreds of rockets into two eastern Afghan provinces over the past three weeks, killing 36 people, including 12 children.

Pakistani army spokesman Maj. Athar Abbas said no rounds have been intentionally fired into Afghanistan. He said it is possible that a few rounds may have accidentally fallen into Afghanistan when security forces targeted militants carrying out cross-border attacks into Pakistan.

The back-and-forth accusations have further strained the troubled relationship between the two countries and could hamper talks between Pakistan, Afghanistan and the U.S. in Kabul on Tuesday. The meeting is meant to focus on reconciliation talks with Taliban militants fighting in Afghanistan.

The Afghan government has repeatedly criticized Pakistan for not targeting Afghan Taliban militants who use its territory to launch cross-border attacks -- an accusation echoed by the U.S. and other NATO countries.

Pakistan has recently reversed this criticism, saying Afghan and NATO forces have not done enough to target Pakistani Taliban militants who have established sanctuaries in eastern Afghanistan and are using them to attack Pakistan.

The Afghan and Pakistani Taliban have close links but different goals. The Afghan Taliban are focused on fighting NATO and Afghan troops in Afghanistan and have close historical links to Pakistan. Many analysts have said Pakistan is reluctant to target the Afghan Taliban because they could be useful allies in Afghanistan after foreign forces withdraw.

In contrast, the Pakistani Taliban are a sworn enemy of Pakistan and are focused on toppling the country's U.S.-allied government.

Abbas, the army spokesman, claimed there have been five cross-border attacks in the last month against Pakistani border posts that have killed 55 paramilitary soldiers and tribal policemen and injured 80 others. The attacks took place in the tribal areas of Bajur and Mohmand and in the settled area of Dir, he said.

"The fleeing militants were engaged by the security forces, and a few accidental rounds going across (into Afghanistan) cannot be ruled out," Abbas said.

Afghan President Hamid Karzai on Sunday accused Pakistan of firing 470 rockets into the eastern provinces of Kunar and Nangarhar and said "they should be stopped immediately."

And "if they are not being carried out by Pakistan, Pakistan should make it clear who is behind the attacks," he said in a statement issued by the presidential palace.

The Pakistani army has said the recent cross-border attacks came from Kunar, an area where NATO has recently withdrawn many of its combat troops.

Karzai said he discussed the rocket barrage with Pakistani President Asif Ali Zadari during an anti-terrorism conference in Tehran on Saturday, the same day the Afghan Defense Ministry spokesman spoke of the attacks and warned that Afghanistan would defend itself.

"The government of Pakistan should understand that there will be a reaction for killing Afghan citizens," said spokesman Mohammad Zahir Azimi.

Saying it was in response to Pakistani fire, Afghan security forces in the eastern provinces of Khost and Paktika launched artillery across the border at least twice on Friday, Azimi said. Afghan security officials said NATO also fired into Pakistan on June 17. NATO and Pakistani military officials earlier denied any knowledge of such border fire from the Afghan side.

The Afghan president said he also discussed the border attack with Afghan NATO commander Gen. David Petraeus and U.S. Ambassador Karl Eikenberry during his regular national security council meeting on Sunday.

Afghan border police spokesman Edris Mohmand, who reported 36 Afghans killed by the rockets, including 12 children, said 2,000 families have fled the Asmar and Nangalam districts of Kunar province and the Goshta district in Nangarhar.

"All these attacks have been from Pakistan's side and for sure they are Pakistani weapons being used against innocent Afghans," Mohmand said. "The border police in the eastern region have been equipped with heavy artillery but we are waiting for orders from the interior minister."