Magnetic fields in galaxies and galaxy clusters are believed to be the result of the amplification of intergalactic seed fields during the formation of large-scale structures in the universe. However, the origin, strength, and morphology of this intergalactic magnetic field (IGMF) remain unknown. Lower limits on (or indirect detection of) the IGMF can be obtained from observations of high-energy gamma rays from distant blazars. Gamma rays interact with the extragalactic background light to produce electron−positron pairs, which can subsequently initiate electromagnetic cascades. The gamma-ray signature of the cascade depends on the IGMF since it deflects the pairs. Here we report on a new search for this cascade emission using a combined data set from the Fermi Large Area Telescope and the High Energy Stereoscopic System. Using state-of-the-art Monte Carlo predictions for the cascade signal, our results place a lower limit on the IGMF of B > 7.1 × 10 G for a coherence length of 1 Mpc even when blazar duty cycles as short as 10 yr are assumed. This improves on previous lower limits by a factor of 2. For longer duty cycles of 10 (10) yr, IGMF strengths below 1.8 × 10 G (3.9 × 10 G) are excluded, which rules out specific models for IGMF generation in the early universe.