A new all-optical microwave photonic notch filter is presented. It is based on controlling the amplitude and phase of the optical carriers and RF phase modulation sidebands via a diffraction-based Fourier-domain optical processor. It has the ability of realizing a flat passband, narrow notch, and large free spectral range amplitude response and a group delay response with very little ripples. The carrier and sideband optical phase controls enable a continuous notch frequency tuning operation to be realized without altering the response shape. The filter has a simple structure and a wide bandwidth as it only involves optical components. Experimental results demonstrate a microwave photonic notch filter that exhibits a flat passband with < 1 dB ripples, a deep notch of > 35 dB and low group delay ripples of < ±25 ps, together with the continuous notch frequency tunability and excellent long term stability and repeatability.