A drill head for an apparatus for directional boring according to the invention includes a bit, a holder for a device for detecting angular orientation of the bit, and a hammer including a striker for delivering impacts to the bit, wherein the bit assembly, holder and hammer are connected head to tail with the bit at a front end. The bit of the invention has a frontwardly facing main cutting surface having a plurality of main cutting teeth disposed thereon and a gage tower extending radially outwardly from the main cutting surface, which gage tower has at least one frontwardly facing gage cutting tooth thereon suitable for cutting over an angle defined by less than a full rotation of the bit. The device for detecting angular orientation is in a predetermined alignment with the gage tower so that it determines the orientation of the gage tower relative to the axis of rotation of the drill head. A starter rod may be used to connect the holder to the string, and the hammer generally follows immediately behind the bit, so that order of components from front to rear is bit, hammer, holder and starter rod. In one preferred embodiment, the main cutting surface is substantially flat and circular and has fluid ejection ports thereon, and the drill head has passages for conducting a drill fluid therethrough to the ejection ports. In another preferred embodiment, the bit has a heel on an outer side surface thereof at a position opposite the gage tower, which heel slopes inwardly from back to front. The heel aids in steering the bit in both rock and soil. Such a drill head can be used for directional boring in mixed conditions including soil, soft rock and even hard rock.