We report here an extension of the measurement of the all-particle cosmic-ray spectrum with IceTop to lower energy. The new measurement gives full coverage of the knee region of the spectrum and reduces the gap in energy between previous IceTop and direct measurements. With a new trigger that selects events in closely spaced detectors in the center of the array, the IceTop energy threshold is lowered by almost an order of magnitude below its previous threshold of 2 PeV. In this paper we explain how the new trigger is implemented, and we describe the new machine-learning method developed to deal with events with very few detectors hit. We compare the results with previous measurements by IceTop and others that overlap at higher energy and with HAWC and Tibet in the 100 TeV range.