Fast radio bursts (FRBs) are millisecond radio pulses originating from powerful enigmatic sources at extragalactic distances. Neutron stars with large magnetic fields (magnetars) have been considered as the sources powering the FRBs, but the connection requires further substantiation. Here we report the detection by the AGILE satellite on 28 April 2020 of an X-ray burst in temporal coincidence with a bright FRB-like radio burst from the Galactic magnetar SGR 1935+2154. The burst observed in the hard X-ray band (18-60 keV) lasted about 0.5 s, it is spectrally cut off above 80 keV and implies an isotropically emitted energy of about 10(40) erg. This event demonstrates that a magnetar can produce X-ray bursts in coincidence with FRB-like radio bursts. It also suggests that FRBs associated with magnetars can emit X-ray bursts. We discuss SGR 1935+2154 in the context of FRBs with low-intermediate radio energies in the range 10(38)-10(40) erg. Magnetars with magnetic fields B approximate to 10(15) G may power these FRBs, and new data on the search for X-ray emission from FRBs are presented. We constrain the bursting X-ray energy of the nearby FRB 180916 to be less than 10(46) erg, smaller than that observed in giant flares from Galactic magnetars.In April 2020, the AGILE satellite registered an X-ray burst temporally coincident with a radio burst from the Galactic magnetar SGR 1935+2154. As seen in hard X-rays, the burst was cut off above 80 keV and had an isotropically emitted energy of about 10(40) erg.
