Primitive meteorites contain isotopes that are the decay products of short-lived nuclides in the early Solar System(1,2). The relative abundances of these isotopes provide a means to determine timescales for the formation and accretion of primitive Solar System objects, the abundances of the parent nuclides being fixed when these objects solidified, The abundances can also be used to investigate the source of the nuclides (such as Ca-41, Al-26, Fe-60, Mn-53 and Pd-107), although this is an area of controversy. The nuclides could have originated from a single stellar object(2-6), such as a nearby red-giant or a supernova. But observations of enhanced ion fluxes in a molecular cloud(7) have led to other models(8-10) in which these nuclides are formed by energetic particle irradiation of gas and dust in the protosolar molecular cloud; alternatively, irradiation by energetic particles from the active early Sun may have occurred within the solar nebula itself(11-18). Here we show that there is a correlation between the initial abundances of Ca-41 and Al-26 in samples of primitive meteorite (as inferred from their respective decay products, K-41 and Mg-26), implying a common origin for the short-lived nuclides. We can therefore rule out the mechanisms based on energetic particle irradiation, as they cannot produce simultaneously the inferred initial abundances of both nuclides. If, as our results suggest, a single stellar source is responsible for generating these nuclides, we can constrain to less than one million years the timescale for the collapse of the protosolar cloud to form the Sun.