The cable was sent by the US ambassador to Yemen, the daily said.
The daily said the remarks prompted Yemen's deputy prime minister to "joke that he had just 'lied' by telling parliament" that Yemeni forces had staged the strikes against Al-Qaeda in the Arabian Peninsula, Al-Qaeda's Yemeni arm.
The Washington Post reported earlier this month that Washington had deployed drones to hunt down jihadists.
With more than 100,000 US troops fighting Al-Qaeda's allies in Afghanistan and public skepticism in Yemen over the US role there, US officials have stressed that Sanaa will lead the fight against Islamist militants.
On November 16, US Defense Secretary Robert Gates said providing equipment and training to Yemeni security forces offered the best way to counter the threat posed by Al-Qaeda militants.