KABUL, Afghanistan — Violence continued to flare in Afghanistan on Sunday, with four more American soldiers reported killed in three incidents.

The buildup of American forces ordered last year by PresidentBarack Obamahas brought more attacks from the Taliban against Western troops and efforts by the extremist group to exert its power in the country.

Two U.S. troops were killed in insurgent attacks in the east and two others died in southern Afghanistan, the most dangerous areas of the country, where most of the new troops have been deployed.

The NATO force did not disclose details about the fatalities, announced on a day in which Afghan PresidentHamid Karzaiagain condemned the stoning deaths last week by Islamist militants of a young Afghan couple who had eloped.

“”I was shocked when I heard that,”” he told ABC’s “”This Week”” withChristiane Amanpour. “”That’s a terrible sign. That’s — that’s indeed part of our failure, the Afghan government and the international community as well, to give protection to the Afghan people.””

Asked about his efforts to get the Taliban to the peace talks, Karzai said there were “”individual contacts with some Taliban elements. That’s not yet a formal process.””

Karzai also reaffirmed his support of a quick removal of private security firms from Afghanistan, accusing them of causing corruption and of harassing Afghans.

“”Their presence is preventing the growth and the development of the Afghan security forces, especially the police force because 40,000, 50,000 people are given more salaries than the Afghan police,”” he said. “”And here, ma’am, through you I am appealing to the U.S. taxpayer not allow their hard-earned money to be wasted on groups that are not only providing lots of inconveniences to the Afghan people, but actually are God knows in contact with Mafia-like groups and perhaps also funding militants and insurgents and terrorists through those firms.””

Karzai’s stance on private security contractors has caused consternation among many in Kabul’s large expatriate community. Almost no one considers Afghan police and soldiers ready to step in and fill the protective role played by private contractors. A shutdown of private security firms in the next four months could also leave the North Atlantic Treaty Organization force scrambling to replace contractors who have helped guard supply convoys and bases.