WASHINGTON — The relatives of three United States citizens killed in American drone strikes without trial, including Anwar al-Awlaki, a radical Muslim cleric, have decided not to appeal a federal judge’s dismissal of a lawsuit they filed against Obama administration officials.

The lawsuit sought unspecified damages against several top national security officials for the deaths from two drone strikes in Yemen in 2011; the victims also included Samir Khan and Mr. Awlaki’s teenage son, Abdulrahman al-Awlaki. In April, Judge Rosemary M. Collyer of the Federal District Court for the District of Columbia dismissed the case, deferring to the government’s national-security arguments.

In a statement, Nasser al-Awlaki, the father of Mr. Awlaki and the grandfather of Abdulrahman, said he had lost faith in the American courts. The older Mr. Awlaki had also sought an injunction blocking the government from trying to kill his son before the drone strike, but a Federal District Court judge dismissed that as well.

“Although the court failed to fulfill its role in this case, my family and I continue to hope that answers to our questions about why our son and grandson were killed will someday see the light of day, and that there may someday be accountability for the government’s actions,” he said.