Using the KEDR detector at the VEPP-4M e+e− collider, we have measured the values of Ruds and R at seven points of the center-of-mass energy between 3.12 and 3.72 GeV. The total achieved accuracy is about or better than 3.3% at most of energy points with a systematic uncertainty of about 2.1%. At the moment it is the most accurate measurement of R(s) in this energy range.