Reporters familiar with Mehsud said the voice appeared to be his.
The recording comes a day after the Taliban released a similar audio file in which Mehsud said he was alive but did not mention the specific raid on Thursday which had triggered rumours of his death.
Conflicting reports has emerged after the attack, with some security officials saying Mehsud was injured and others saying he and some of his senior commanders were probably killed.
Richard Holbrooke, the US special envoy to Pakistan and Afghanistan, said the US did not know if Mehsud had been killed.
"I've heard every conceivable version of what's happened and I don't know," he said on Saturday while visiting Afghanistan.
"But if he's still alive he's one of the worst people on earth. Absolutely vicious."
The Taliban has issued a number of statements denying Mehsud's death, and Azam Tariq, one of their spokesmen, said his boss had left the Shaktoi area struck by the missiles "40 to 60 minutes" before the raid.
"Hakimullah is alive and safe. I met with him last night, there was not even a scratch on him," Tariq told the AFP news agency on Friday.
Another Taliban official however said Mehsud had been injured in the attack.
Mehsud took over as leader of the Pakistani Taliban five months ago, after Baitullah Mehsud, his predecessor, was killed in a drone attack.
The Taliban denied Baitullah Mehsud's death for weeks, apparently amid fierce infighting over his successor.
The US does not confirm drone attacks, but its forces in neighbouring Afghanistan and the Central Intelligence Agency are the only ones known to use the unmanned aircraft capable of firing missiles.