The current research was focused on the extracellular biosynthesis of bactericidal silver nanoparticles (AgNPs) using cell-free supernatant of a local isolate previously identified as a novel Streptomyces aegyptia NEAE 102. The biosynthesis of silver nanoparticles by Streptomyces aegyptia NEAE 102 was quite fast and required far less time than previously published strains. The produced particles showed a single surface plasmon resonance peak at 400 nm by UV-Vis spectroscopy, which confirmed the presence of AgNPs. Response surface methodology was chosen to evaluate the effects of four process variables ($AgNO_3$ concentration, incubation period, pH levels, and inoculum size) on the biosynthesis of silver nanoparticles by Streptomyces aegyptia NEAE 102. Statistical analysis of the results showed that the linear and quadratic effects of incubation period, initial pH, and inoculum size had a significant effect (p < 0.05) on the biosynthesis of silver nanoparticles by Streptomyces aegyptia NEAE 102. The maximum silver nanoparticles biosynthesis (2.5 OD, at 400 nm ) was achieved in runs number 5 and 14 under the conditions of 1 mM $AgNO_3$ (1-1.5% (v/v)), incubation period (72-96 h), initial pH (9-10), and inoculum size (2-4% (v/v)). An overall 4-fold increase in AgNPs biosynthesis was obtained as compared with that of unoptimized conditions. The biosynthesized silver nanoparticles were characterized using UV-VIS spectrophotometer and Fourier transform infrared spectroscopy analysis, in addition to antimicrobial properties. The biosynthesized AgNPs significantly inhibited the growth of medically important pathogenic gram-positive (Staphylococcus aureus) and gram-negative bacteria (Pseudomonas aeruginosa) and yeast (Candida albicans).