The Obama administration did not initially raise objections when Qatar began shipping arms to opposition groups in Syria, even if it did not offer encouragement, according to current and former administration officials. But they said the United States has growing concerns that, just as in Libya, the Qataris are equipping some of the wrong militants.

The United States, which had only small numbers of C.I.A. officers in Libya during the tumult of the rebellion, provided little oversight of the arms shipments. Within weeks of endorsing Qatar’s plan to send weapons there in spring 2011, the White House began receiving reports that they were going to Islamic militant groups. They were “more antidemocratic, more hard-line, closer to an extreme version of Islam” than the main rebel alliance in Libya, said a former Defense Department official.

The Qatari assistance to fighters viewed as hostile by the United States demonstrates the Obama administration’s continuing struggles in dealing with the Arab Spring uprisings, as it tries to support popular protest movements while avoiding American military entanglements. Relying on surrogates allows the United States to keep its fingerprints off operations, but also means they may play out in ways that conflict with American interests.

“To do this right, you have to have on-the-ground intelligence and you have to have experience,” said Vali Nasr, a former State Department adviser who is now dean of the Paul H. Nitze School of Advanced International Studies, part of Johns Hopkins University. “If you rely on a country that doesn’t have those things, you are really flying blind. When you have an intermediary, you are going to lose control.”

He said that Qatar would not have gone through with the arms shipments if the United States had resisted them, but other current and former administration officials said Washington had little leverage at times over Qatari officials. “They march to their own drummer,” said a former senior State Department official. The White House and State Department declined to comment.