C172 Flight Instructor who reported loss of engine power on initial climb was able to descend back down and land.

Narrative

*Newly installed; Continental O-300-D engine. It has approximately 10 hours on it and is still in its 'break-in' period of 25 hours. In turn; gentle handling is a must. *NWKRAFT; W&B; etc. completed.1. Pre-flight Action and Runup (Normal) - I checked the cylinder head temps to ensure they were within the approved range for the new engine2. During pre-flight brief; student to fly and I (instructor) to monitor and communicate with Tower (ZZZ)3. Upon approaching runway; I notified the tower 'May we please have full stop; taxi backs; as this is a break-in flight for the engine' and tower approved4. Student taxied onto the runway and confirmed 'all instruments are in the green' and verified by me; so we proceeded with the takeoff5. Student applied full power; we reached ~63mph and he rotated6. We were climbing out at approximately 80 mph when we began losing vertical speed at 50 ft AGL and leveled7. I instructed my student; 'apply full power' and he responded 'I have full power in'8. I stated; 'my controls' and we used positive exchange of controls9. I then verified he had; in fact; applied full power and that's when we began losing airspeed10. I lowered the pitch to gain airspeed; and then attempted a brief climb again; to no avail11. At that point; I was forced to make a decision because I was staring at a treeline at the end of the runway12. I contacted the tower and said 'I need to abort this takeoff' and tower responded 'Roger that. Clear to land.'13. I pulled the carb heat on; idled the power; and begin to step the plane down; while attempting intermittently to bleed off airspeed (as I had limited runway). I requested my student make airspeed call outs; so I could ensure we touched down at a safe speed.14. I held the plane off the runway long enough to get below 60 mph and touched down on the mains and rolled to the end of the runway before exiting15. The tower asked if I wanted them to hold my chip / stay with them and re-attempt a pattern entry; and I declined16. I taxied to the ramp; and we exited the aircraft17. Upon inspection; we noticed there was a faint burning scent emanating from near the spinner. We checked inside the cowling via the oil door and it was less strong.18. I contacted our maintenance mechanic and downed the aircraft; so it will not be flown until further inspection and release