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The astrophysical 6Li(p,γ)7Be reaction occurs during Big Bang nucleosynthesis and the pre-main sequence and main sequence phases of stellar evolution. The low-energy trend of its cross section remains uncertain, since different measurements have provided conflicting results. A recent experiment reported a resonance-like structure at center-of-mass energy 195 keV, associated to a positive-parity state of 7Be. The existence of such resonance is still a matter of debate. We report a new measurement of the 6Li(p,γ)7Be cross section performed at the Laboratory for Underground Nuclear Astrophysics, covering the center-of-mass energy range E = 60 - 350 keV. Our results rule out the existence of low-energy resonances. The astrophysical S-factor varies smoothly with energy, in agreement with theoretical models.