A comprehensive catalogue of historical earthquakes, with accurate epicentres and harmonised magnitudes is a crucial resource for seismic hazard mapping. Here we update and combine catalogues from several sources to compile a catalogue of earthquakes in and near Iceland, in the years 1900–2019. In particular the epicentres are based on local information, whereas the magnitudes are based on teleseismic observations, primarily from international on-line catalogues. The most reliable epicentre information comes from the catalogue of the Icelandic Meteorological Office, but this is complemented with information from several technical reports, scientific publications, and newspaper articles. The catalogue contains 1281 moment magnitude (MW) ≥ 4 events and the estimated completeness magnitude is MW 5.5 in the first years, going down to MW 4.5 for recent years. The largest magnitude is MW 7.0. Such merging of local data and teleseismic catalogues has not been done before for Icelandic earthquakes, and the result is an earthquake map with much more accurate locations than earlier maps. The catalogue also lists additional 5640 earthquakes on the Mid-Atlantic Ridge, north of 43°, with both epicentres and magnitudes determined teleseismically. When moment magnitudes are not available, proxy MW values are computed using chi-squared-regression, normally on the surface-wave magnitude, but exceptionally on the body-wave magnitude. Magnitudes MW ≥ 4.5 have associated uncertainty estimates. The actual combined seismic moment released in the Icelandic earthquakes is found to be consistent with the moment estimated using a simple plate motion model, indicating that the seismic activity of the catalogue period might be typical for any 120 year timespan. The catalogue is named ICEL-NMAR and it is available online on http://data.mendeley.com.