Can US President reclassify firearms by executive order?

I had recently read a opinion piece wherein the author was suggesting that certain firearms could be reclassified to Class 3 Firearms and that doing so was not violating the Constitution, but would require registration of such firearms.

Is this feasible, and could a reclassification be done by executive order (similar to the Executive Order on bump stocks)?

ETA: this question never mentions reclassification of semi-automatic to fully automatic (as has been the basis of some answers). Some class 3 weapons are not full automatic but appears to be so classified for other reasons ie short barreled shotguns or cane guns)