In the WIMP scenario, there is a one-to-one relation between the dark matter (DM) relic density and spin independent direct detection rate if both the annihilation of DM and its elastic scattering on nuclei go dominantly through Higgs exchange. In particular, for DM masses much smaller than the Higgs boson mass, the ratio of the relevant cross sections depends only on the DM mass. Assuming DM mass and direct detection rate within the ranges allowed by the recent DAMA collaboration results -taking account of the channelling effect on energy threshold and the null results of the other direct detection experiments-gives a definite range for the relic density. For scalar DM models, like the Higgs portal models or the inert doublet model, the relic density range turns out to be in agreement with WMAP. This scenario implies that the Higgs boson has a large branching ratio to pairs of DM particles, a prediction which might challenge its search at the LHC.The DAMA collaboration has recently provided evidence for an annual modulation of the rate of nuclear recoils in their detector [1], confirming at a firmer level their previous results [2]. Taking into account the null results of the other direct Dark Matter (DM) detection experiments [3] and the recently discovered channelling effect on the threshold energy in DAMA, points towards a nuclear recoil due to dark matternucleon elastic scatterings, with a spin independent (SI) cross section in the range (see [4])and dark matter mass in the range 3 GeV m DM 8 GeV.These results have been already the object of various studies in specific models [5,6,7,8]. In this short letter, working in the WIMP framework which assumes a DM relic density determined by the thermal freeze-out of DM annihilation, we emphasize the importance of Higgs exchange diagrams for DM mass in the range of (2). If the DM candidate is light, there is a limited number of possible (2-body) annihilation channels to SM particles, i.e. the Inert Doublet Model (IDM), a two Higgs model extension of the Standard Model with a scalar dark matter candidate [10,11,12,13,14,15,16], and a fortiori for a singlet scalar DM candidate [17,18,19,20,21,22,23,24], the channels of Fig.1 are the only possible non-negligible ones in the range of (2). In more sophisticated models, such as with the neutralino DM candidate of the MSSM, these channels coexist a priori with many other channels, in particular with other intermediate Higgs scalar particle or squarks channels [7,25].Both processes in Fig.1 are tightly related. The Higgs boson mass dependence is the same, mh , because in both cases the momentum of the Higgs is negligible compared with m h . Furthermore the dependence in the unknown DM-DM-h coupling is the same. This means that, up to uncertainties in the Yukawa couplings of the SM fermions and in the Higgs to nucleon coupling, the only left parameter is the mass of the dark matter. This dependence is however limited if we take the DM mass within the range (2). In other words, if Higgs mediated processes are dominant, the r...