Stellar X-ray emission plays an important role in the study of exoplanets as a proxy for stellar winds and as a basis for the prediction of extreme ultraviolet (EUV) flux, unavailable for direct measurements, which in their turn are important factors for the mass-loss of planetary atmospheres. Unfortunately, the detection thresholds limit the number of stars with the directly measured X-ray fluxes. At the same time, the known connection between the sunspots and X-ray sources allows using of the starspot variability as an accessible proxy for the stellar X-ray emission. To realize this approach, we analysed the light curves of 1729 main-sequence stars with rotation periods 0.5<P<30d and effective temperatures 3236<Teff<7166K observed by the Kepler mission. It was found that the squared amplitude of the first rotational harmonic of a stellar light curve may be used as a kind of activity index. This averaged index revealed practically the same relation with the Rossby number as that in the case of the X-ray to bolometric luminosity ratio R_x_. As a result, the regressions for stellar X-ray luminosity L_x_(P, T_eff_) and its related EUV analogue L_EUV_ were obtained for the main-sequence stars. It was shown that these regressions allow prediction of average (over the considered stars) values of log(L_x_) and log(L_EUV_) with typical errors of 0.26 and 0.22dex, respectively. This, however, does not include the activity variations in particular stars related to their individual magnetic activity cycles.