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The Atmosphere‐Space Interactions Monitor was designed to monitor Terrestrial Gamma‐ray Flashes (TGFs) and Transient Luminous Events (TLEs) from space, enabling the study of how these phenomena are related. In this paper, we present observations of 17 TGFs with accompanying Elves. TGFs are short and highly energetic bursts of gamma photons associated with lightning discharges, whereas Elves are TLEs that are observed as concentric rings of ultraviolet (UV) and visible light at ionospheric altitudes, produced by the excitation of N2 molecules when an electromagnetic pulse hits the base of the ionosphere. Elves were identified when optical detections in the UV band could be clearly distinguished from other optical signals from lightning strokes. The TGFs they accompanied had short durations and were associated with particularly high peak current lightning. Lightning sferics associated with these events were detected by the global lightning network GLD360 and the World Wide Lightning Location Network, and they were, with the exception of one event, observed over ocean or coastal regions. It is likely that these events were associated with Energetic In‐cloud Pulses. We show that short duration TGFs tend to be associated with higher peak currents than long duration TGFs. Key Points: We present a sample of 17 Terrestrial Gamma‐ray Flashes (TGFs) with accompanying Elves detected by Atmosphere‐Space Interactions MonitorTGFs with Elves are short and associated with very high peak current lightningThe peak currents for these events are higher than for both lightning and TGFs in general [ABSTRACT FROM AUTHOR]