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WASHINGTON — In the spring of 2010, Afghan officials struck a deal to free an Afghan diplomat held hostage by Al Qaeda. But the price was steep — $5 million — and senior security officials were scrambling to come up with the money.

They first turned to a secret fund that the Central Intelligence Agency bankrolled with monthly cash deliveries to the presidential palace in Kabul, according to several Afghan officials involved in the episode. The Afghan government, they said, had already squirreled away about $1 million from that fund.

Within weeks, that money and $4 million more provided from other countries was handed over to Al Qaeda, replenishing its coffers after a relentless C.I.A. campaign of drone strikes in Pakistan had decimated the militant network’s upper ranks.Bin Laden urged caution, fearing the Americans knew about the payment and had laced the cash with radiation or poison, or were tracking it. “There is a possibility — not a very strong one — that the Americans are aware of the money delivery,” he wrote back, “and that they accepted the arrangement of the payment on the basis that the money will be moving under air surveillance.”