Small-angle neutron scattering spectra from supercritical heavy water were recorded along a near-critical isochore at temperatures between (T-c,T-exp+1.63 K) and (T-c,T-exp+22.02 K), T-c,T-exp being the experimental critical temperature. At low values of the wave number transfer q, the scattered intensity shows a pronounced increase due to the divergence of density fluctuations at the critical point. In the studied q range, from 0.07 to 0.36 Angstrom(-1), all the spectra can be accurately described by the Fisher-Langer correlation function provided that a multiplicative additional term describing short-range correlations between water molecules is taken into account. The value found for the amplitude of the critical correlation length is xi(0)=(1.36 +/- 0.06) Angstrom, in fair agreement with the value predicted by the two-scale hypothesis.