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Some accreting binary systems containing a white dwarf (such as classical novae or persistent supersoft sources) are seen to emit low-energy X-rays with temperatures of ~10^6 K and luminosities exceeding 10^35 erg/s. These X-rays are thought to originate from nuclear burning on the white dwarf surface, either caused by a thermonuclear runaway (classical novae) or a high mass-accretion rate that sustains steady nuclear burning (persistent sources). The discovery of transient supersoft X-rays from ASASSN-16oh challenged these ideas, as no clear signatures of mass ejection indicative of a classical nova eruption were detected, and the origin of these X-rays remains controversial. It was unclear whether this star was one of a kind or representative of a larger, as yet undiscovered, group. Here, we present the discovery of 29 stars located in the direction of the Magellanic Clouds exhibiting long-duration, symmetrical optical outbursts similar to that seen in ASASSN-16oh. We observed one of these objects during an optical outburst and found it to be emitting transient supersoft X-rays, while no signatures of mass ejection (indicative of a classical nova eruption) were detected. We therefore propose that these objects form a homogeneous group of transient supersoft X-ray sources, which we dub ``millinovae'' because their optical luminosities are approximately a thousand times fainter than those of ordinary classical novae.