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We study a classically scale-invariant model with an electroweak singlet scalar mediator together with a scalar dark matter multiplet of global O(N) symmetry. Our most general conformally invariant scalar potential generates the electroweak symmetry breaking via the Coleman-Weinberg mechanism, and the new scalar singlet acquires its mass through radiative corrections of the SM particles and the scalar dark matter. Taking into account the collider bounds, we present the allowed region of new physics parameters satisfying the recent measurement of relic abundance. With the obtained parameter sets, we predict the elastic scattering cross section of the new scalar multiplet into target nuclei for a direct detection of the dark matter. We also perform a full analysis with arbitrary set of parameters for N≥2, and discuss the implication of the constraints from the on-going direct and indirect detections of dark matter.