We calculate the flux of ␥ rays emitted from primordial black holes ͑PBHs͒ which are formed by a ''blue'' power-law spectrum of density fluctuations in the early universe. Gamma-ray emission from such PBHs may contribute significantly to the observed extragalactic diffuse ␥-ray background ͑DGB͒. Using the observed DGB flux from the imaging Compton Telescope ͑COMPTEL͒ and the Energetic Gamma Ray Experiment Telescope ͑EGRET͒ as the upper limit of ␥-ray flux from PBHs, we derive the upper limit on the spectral index n of the density fluctuations. The range of initial PBH masses which can contribute to the DGB is 2 ϫ10 13 gϪ5ϫ10 14 g, corresponding to a cosmic reheating temperature of 7ϫ10 7 GeVϪ4ϫ10 8 GeV. In this range, we find the upper limit to be nՇ1.23Ϫ1.25. This limit is stronger than those derived from the energy density in PBHs or PBH relics and matches the value of n required to explain the cosmic microwave background anisotropy. ͓S0556-2821͑99͒05804-X͔ PACS number͑s͒: 95.85.Pw, 97.60.Lf, 98.80.Es