“How old are these people?” he asked, according to two officials present. “If they are starting to use children,” he said of Al Qaeda, “we are moving into a whole different phase.”

It was not a theoretical question: Mr. Obama has placed himself at the helm of a top secret “nominations” process to designate terrorists for kill or capture, of which the capture part has become largely theoretical. He had vowed to align the fight against Al Qaeda with American values; the chart, introducing people whose deaths he might soon be asked to order, underscored just what a moral and legal conundrum this could be.

Mr. Obama is the liberal law professor who campaigned against the Iraq war and torture, and then insisted on approving every new name on an expanding “kill list,” poring over terrorist suspects’ biographies on what one official calls the macabre “baseball cards” of an unconventional war. When a rare opportunity for a drone strike at a top terrorist arises — but his family is with him — it is the president who has reserved to himself the final moral calculation.

“He is determined that he will make these decisions about how far and wide these operations will go,” said Thomas E. Donilon, his national security adviser. “His view is that he’s responsible for the position of the United States in the world.” He added, “He’s determined to keep the tether pretty short.”