When a weak absorber is placed inside the cavity of a broadband untuned dye laser a strong enhancement of the extinction is observed. This effect is investigated quantitatively for the absorption of the Na-D1 line by sodium atoms dispersed in a flame. A set of laser rate equations containing the known stimulated emission cross sections as well as the absorption cross sections for both the ground and the triplet state, is used to determine the spectral and temporal behavior of the laser action and of the enhancement effect. Theoretical and experimental results are in agreement within the limits of error. This intracavity absorption enhancement technique offers particular advantages for the detection of short-lived intermediate species. Its sensitivity is not likely to be matched by other absorption methods.