PANJWAI, Afghanistan — Stalking from home to home, a United States Army sergeant methodically killed at least 16 civilians, 9 of them children, in a rural stretch of southern Afghanistan early on Sunday, igniting fears of a new wave of anti-American hostility, Afghan and American officials said.

Residents of three villages in the Panjwai district of Kandahar Province described a terrifying string of attacks in which the soldier, who had walked more than a mile from his base, tried door after door, eventually breaking in to kill within three separate houses. The man gathered 11 bodies, including those of 4 girls younger than 6, and set fire to them, villagers said.

Coming after a period of deepening public outrage, spurred by the Koran burning by American personnel last month and an earlier video showing American Marines urinating on dead militants, the possibility of a violent reaction to the killings added to a feeling of siege here among Western personnel. Officials described growing concern over a cascade of missteps and offenses that has cast doubt on the ability of NATO personnel to carry out their mission and has left troops and trainers increasingly vulnerable to violence by Afghans seeking revenge.

President Hamid Karzai condemned the attacks, calling them in a statement an “inhuman and intentional act” and demanding justice. Both President Obama and Defense Secretary Leon E. Panetta called Mr. Karzai, expressing condolences and promising thorough investigations. “This incident is tragic and shocking, and does not represent the exceptional character of our military and the respect that the United States has for the people of Afghanistan,” Mr. Obama said in a statement.