First results on the energy spectrum and flux of reactor antineutrinos as a function of the distance L from the reactor core, measured in the Neutrino-4 experiment for 6 < L < 12 m, are presented. The flux L‑dependence fits to the 1/L2 form with a statistical significance of ~10% corresponding to 1.64σ, so that the measured spectrum deviates from the 1/L2 law at a confidence level ~90%. The measured energy spectrum deviates from the predicted one at a similar confidence level ~90%. That both deviations are best described with oscillation parameters in the same regions of $$\Delta m_{{14}}^{2} \approx 0.7{\text{-}}0.8$$ eV2and $${{\sin }^{2}}2{{\Theta }_{{14}}} \approx 0.10{\text{-}}0.15$$ boosts the overall confidence level to ~95% (2σ). These results suggest that antineutrinos oscillate to a sterile state, but still fall short of reliably establishing the oscillation phenomenon. At present, the possibility of mimicking the oscillation effect by systematic errors cannot be completely excluded.