Nairobi, Sept. 17 -- The United States military is seeking powers to carry out covert drone strikes in Kenya, a far-reaching proposal that would for the first time hand Washington military leeway to directly conduct counterterrorism combat operations within the Kenyan territory.

A report by the New York Times published on Tuesday quoted senior officials saying the US military's Africa Command is pressing for new authorities to carry out armed drone strikes targeting Al Qaeda-linked Al Shabab fighters in portions of eastern Kenya, potentially expanding the warzone across the border from their sanctuaries in Somalia.

The push for the expanded authorities, the report said, traces back to a Shabab terrorist attack on the US military base in L...