A new all-optical microwave photonic notch filter (MPNF) 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 few 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 an MPNF 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.