President Obama met privately with the Dalai Lama, the exiled spiritual leader of Tibet, at the White House on Saturday, despite a warning from Beijing that the meeting would risk damaging relations between China and the United States.

Reflecting the diplomatic delicacy of the visit, the 44-minute meeting with the Dalai Lama — Mr. Obama’s second as president — was closed to the news media. China considers Tibet its territory and the Dalai Lama a separatist, although he favors self-rule rather than independence.