C172 flight instructor on a training flight with student reported an engine malfunction after takeoff resulting in a return to the departure airport.

Narrative

Engine partial failure/ power losses in the Upwind. During the takeoff the student was performing the flight from Runway XX; after Vr; CFI noticed the RPM is slightly lower than normal day (was at 2300; supposed to be around 2400-2500] but it was not a hot day could affect the engine performance. The CFI asked student to check power position and verify at Max power. At around 400ft; RPM dropped to around 2200RPM and climb rate was around 0-100FPM. The CFI asked student to max pitch climb at Vx. At around 500ft; RPM dropped and was not stable. The RPM gage was showing 1900-2100 RPM with moving aggressively. At this point; the airplane could only be maintained at 500 and not able to climb. And CFI took over the control and started to making teardrop maneuver. CFI reported issues and requested 180 back to ZZZ Tower. Since the Tower did not respond; CFI made another radio call. The CFI landed the plane safely from opposite side on the Runway (XX). After landing CFI taxi the plane back to the ramp without additional safety issues.