C172 instructor pilot reported a loss of power during initial climb. The instructor asked the Tower Controller for a return to the airport. A safe landing was accomplished.

Narrative

Loss of power during initial climb right after takeoff: This morning I was doing a regular instruction flight with my student at ZZZ airport. We spent some time doing the pre-flight and making sure the aircraft was in good condition. We drained the tanks and there wasn't water in them. We taxied out to Runway XR via Taxiway X; XX to XR and we did the before takeoff checklist that we usually do (run up) at 1800 rpm; we went through the checklist and the oil pressure was in the green arc; oil temperature was good as well. We checked both magnetos and they both had a drop indication of no more than 125 rpms in each one. Everything seemed fine so we decided to go. We call the Tower and we were cleared for takeoff. I was doing the take off because it was the second flight of my student so I aligned the airplane with the runway centerline and I applied full power gently. During the takeoff roll the oil pressure was good and the oil temperature was good; I reached rotation speed having about 2500 rpm so I rotated and started climbing but when I was at about 200 ft. I noticed we were climbing a little slower than usual so I took a look to the airspeed and I realized I wasn't able to maintain a climb at the best rate of climb speed so I looked at my instruments and took a minute to analyze what was happening; suddenly I noticed that the rpm's needle went down to 1800 and came back to 2000 rpm so I immediately thought to abort the climb and land back on the remaining runway but I was already too high to take that decision so instead I decided to keep going and turn back if I could but by that time I couldn't climb anymore so I called the Tower and told them we needed to come back and land on Runway XXR; I turn left maintained positive control of the aircraft while they cleared us to land and we landed safely on Runway XXR without any further issues; Tower asked us if we required any assistance I said no and we then taxied back to our spot.