Using the KEDR detector at the VEPP-4M $e^+e^-$ collider, we have measured the values of $R_{text{uds}}$ 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.