Accurate and noninvasive measurement of tissue optical properties can be used for biomedical diagnostics and monitoring of tissue analytes. Noninvasive measurement of tissue optical properties (total attenuation and scattering coefficients, optical thickness, etc.) can be performed with the optical coherence tomography (OCT) technique. However, speckle noise substantially deteriorates the accuracy of the measurements with this technique. We studied suppression of speckle noise for accurate measurement of backscattering signal and scattering coefficient with the OCT technique. Our results demonstrate that the precision of measurement of backscattering signals with the OCT technique can be 0.2% for homogeneously scattering media and 0.7% for skin, if spatial averaging of speckle noise is applied. This averaging allows us to achieve the precision of tissue scattering coefficient measurements of approximately +/-0.8%. This precision can be further improved by a factor of 2-3, upon optimization of OCT operating parameters.