WASHINGTON -- The Obama administration is moving toward a hybrid strategy in Afghanistan that would combine elements of both the troop-heavy approach sought by its top military commander and a narrower option backed by Vice President Joe Biden, a decision that could pave the way for thousands of new U.S. forces.

The emerging strategy would largely rebuff proposals to maintain current troop levels and rely on unmanned drone attacks and elite special-operations troops to hunt individual militants, an idea championed by Mr. Biden....