A diode-laser-based technique has been developed for absolute line strength measurements with high precision and accuracy, combining a spectroscopic determination of the integrated absorbance with an optical measurement of the absorption path length by means of a Michelson interferometer. This method has been applied to several {sup 12}C{sup 16}O{sub 2} vibrorotational transitions belonging to the {nu}{sub 1}+2{nu}{sub 2}{sup 0}+{nu}{sub 3} combination band, in the spectral region around 2 {mu}m. The 1{sigma} overall accuracy in line strength determination ranges between 0.4% and 0.7%, while the experimental reproducibility is estimated to be around 0.1%. To our knowledge, these levels are the highest ever reached before. The pressure-broadening coefficients for the same transitions are also reported.