Air carrier Captain reported an unstabilized approach in visual conditions; which resulted in a low altitude alert issued by the tower. The flight leveled out then resumed the approach to a landing.

Narrative

During the RNAV GPS to runway 15 we were configured early due to having to bleed off speed and energy from a high energy approach. As we passed the IAF we were still a few hundred feet above the path and I deselected the autopilot to hand fly and attempt to return to the path prior to crossing the FAF. I was successful in getting the aircraft back on path and configured prior to the FAF in order to continue the approach. As we subsequently continued our approach toward the airport at about 1100 feet I did a crosscheck of the runway and noticed a below glide path indication i processed and reacted at about 1000 feet and leveled off. We were flaps 40 due to the short runway (long one closed for construction) so as I started to level off our airspeed started to decay rapidly. I countered with power and saw a low airspeed around 138 knots which was right at ref. As all this was happening we received an altitude alert from tower. We acknowledged we were correcting. I reintercepted the path based on the visual approach indicators and continued the approach and landing with no other issues. At the time of the approach I had no idea what or why the vertical guidance put us below the path but upon reflection I believe we may have failed to verify low vertical speed at the FAF due to cockpit workload associated with the high energy approach and ATC interactions. This is the only reason I can think of for this to have occurred. can. I believe I did put the aircraft in VNAV but I have no way to know for sure readily available to me. I am thankful that I was cross checking the runway visually and had enough time and SA (Situational Awareness) to prevent any further deviations from our desired path and speed. In hindsight; a go around may have been prudent but again at the time I believed us to be stabilized and in a safe position to land. Additionally we were bumping up against the airfield closing and a possible divert if we did not land in time. The FO and I debriefed and could not immediately identify what caused the below path condition.