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A federal judge on Friday sharply and repeatedly challenged the Obama administration’s claim that courts have no power over targeted drone killings of American citizens overseas.

Judge Rosemary M. Collyer of the United States District Court here was hearing the government’s request to dismiss a lawsuit filed by relatives of three Americans killed in two drone strikes in Yemen in 2011: Anwar al-Awlaki, the radical cleric who had joined Al Qaeda in the Arabian Peninsula; Mr. Awlaki’s 16-year-old son, Abdulrahman, who had no involvement in terrorism; and Samir Khan, a 30-year-old North Carolina man who had become a propagandist for the same Qaeda branch.