We report the generation of 4.3 fs, 1 mJ pulses at 1 kHz using a hollow-core fiber compressor seeded with circularly polarized laser pulses. We observe up to 30% more energy throughput compared to the case of linearly polarized laser input, together with significantly improved output spectral stability. Seeding with circularly polarized pulses proves to be an effective approach for high-energy operation of the hollow-fiber compression technique.