Soft X-ray solar bursts were investigated in the framework of the Interball—Tail Probe project by using an RF-15I-2 X-ray photometer. When studying microflares over the period from September to December 1995, weak bursts with intensities of less than 10−8 W/m2 were detected. All these data are confirmed by observations performed in the framework of the GOES project. The characteristics of solar microflares were determined, and the physical mechanism of weak solar events was considered. The distribution of microflares over their intensities was obtained. It is found that the distribution of solar flares over released energies do not obey a power law, and a lower limit is revealed in this distribution. This result is confirmed by the data obtained in the framework of the RHESSI project. Correlation between the daily average values of the maximum intensities of X-ray bursts of different classes of microflares and the daily average values of the thermal background of the solar corona is revealed.