Throughout the spring, the administration had effectively turned a blind eye as Qatar and the United Arab Emirates supplied the rebels with lethal assistance, according to Mr. Gates and others. But Mrs. Clinton had grown increasingly concerned that Qatar, in particular, was sending arms only to certain rebel factions: militias from the city of Misurata and select Islamist brigades.

She could hardly tell Qatar to stand down if the United States was unwilling to step in with lethal assistance of its own, one State Department aide said, “because their answer would be, ‘Well, those guys need help — you’re not doing it.’” Her view, often relayed to her staff, was that to have influence with the fractious opposition and Arab allies, you had to have “skin in the game,” Mr. Ross said.

Former President Bill Clinton had publicly noted in April 2011 that the United States should “not rule out” arming the opposition, and in emails with Mr. Sullivan, her policy adviser, Mrs. Clinton discussed using private contractors to do just that. Mr. Ross, speaking generally, said she had frequently consulted her husband: “I’d say, ‘Here’s what I think we should do.’ She’d say, ‘That’s what Bill said, too.’”

Now Mrs. Clinton took what one top adviser called “the activist side” of the debate over whether to counter Qatar by arming more secular fighters.

“If you didn’t,” Mr. Ross recalled her arguing, “whatever happened, your options would shrink, your influence would shrink, therefore your ability to affect anything there would also shrink.”

But other senior officials were wary. NATO’s supreme allied commander, Adm. James G. Stavridis, had told Congress of “flickers” of Al Qaeda within the opposition. Mr. Donilon, Mr. Obama’s national security adviser, argued that the administration could not ensure that weapons intended for “the so-called good guys,” as one State Department official put it, did not fall into the hands of Islamist extremists.

In fact, there was reason to worry. Mr. Jibril himself described in an interview how a French shipment of missiles and machine guns had gone awry. At a June meeting, President Sarkozy had agreed to “ask our Arab friends” to supply the Transitional National Council with the weapons, Mr. Jibril said. But, he said, the acting defense minister diverted them to a militia led by Abdel Hakim Belhaj, a militant Islamist who had once been held in a secret prison by the C.I.A.