Insurgents in Afghanistan have killed four NATO troops and two Afghan civilians in separate attacks, while a NATO airstrike killed dozens of Taliban militants in the country's east.

NATO said the three soldiers from New Zealand were killed Sunday in a bomb attack in eastern Afghanistan. It did not provide further details. In southern Afghanistan, a person wearing an Afghan police uniform shot and killed a NATO service member. NATO did not release the names of the victims.

In another attack, insurgents opened fire on members of an Afghan family at a cemetery in the southern town of Lashkar Gah, killing two people and wounding seven others, including women and children. The Afghans were visiting the graves of relatives to mark the Eid al-Fitr festival that ends the Muslim fasting month of Ramadan.

NATO said it carried out an airstrike on Taliban militants engaging in hostile activity in the eastern province of Kunar on Saturday, killing dozens of heavily-armed fighters including a local Taliban leader. It said no civilians were harmed in the airstrike.

In a speech to mark Sunday's Eid festivities, Afghan President Hamid Karzai called on Taliban leaders to renounce violence against civilians carried out in the name of the Islamist group. He said the enemies of Islam committed “cruel” attacks during Ramadan and will one day be held accountable.

NATO's top commander in Afghanistan, U.S. General John Allen, said thousands of insurgents already have renounced violence and returned home to find “honor and dignity” in their communities. In a holiday greeting, General Allen also said Afghanistan's more than 300,000 security personnel have become “capable and professional” and soon will have primary responsibility for areas where the majority of Afghans live.

But, Afghan security forces face a growing threat of infiltration by insurgents. In a series of attacks this month, Afghan security personnel or gunmen disguised in security uniforms have attacked NATO troops, killing at least eight Americans.

U.S. Defense Secretary Leon Panetta discussed the issue of “insider attacks” with Mr. Karzai in a phone call on Sunday. The Defense Department said Panetta urged Mr. Karzai to boost counterintelligence cooperation with NATO, introduce more rigorous vetting of Afghan security recruits and engage in more dialogue with village elders who can vouch for such recruits.

The Pentagon said Mr. Karzai and Panetta agreed that U.S. and Afghan officials should work even more closely together to minimize the potential for future “insider attacks,” which have killed at least 39 coalition personnel this year.