The instrument and methods for measuring spectral parameters of discrete atmospheric lines and water-related continuum absorption in the millimeter wave range are described. The instrument is based on measurements of the Fabry-Pérot resonance response width using fast phase continuous scanning of the frequency-synthesized radiation. The instrument allows measurement of gas absorptions at the cavity eigenfrequencies ranging from 45 to 370 GHz with the highest to date absorption variation sensitivity of 4x10(-9) cm(-1). The use of a module of two rigidly bounded maximum identical resonators differing in length by exactly a factor of two allows accurate separation of the studied gas absorption and spectrometer baseline, in particular, the absorption by water adsorbed on the resonator elements. The module is placed in a chamber with temperature controlled between -30 and +60 degrees C, which permits investigation of temperature dependence of absorption. It is shown that systematic measurement error of discrete atmospheric line parameters does not exceed the statistical one and the achieved accuracy satisfies modern demands for the atmospheric remote sensing data retrieval. Potential systematic error arising from the neglect of the effect of water adsorption on mirror surfaces is discussed. Examples of studies of water and oxygen spectral line parameters as well as continuum absorption in wet nitrogen are given.