Unsteady numerical simulations of axisymmetric reactive jets with one-step Arrhenius kinetics are used to investigate the problem of deflagration initiation in a premixed fuel-air mixture by the sudden discharge of a hot jet of its adiabatic reaction products. For the moderately large values of the jet Reynolds number considered in the computations, chemical reaction is seen to occur initially in the thin mixing layer that separates the hot products from the cold reactants. This mixing layer is wrapped around by the starting vortex, thereby enhancing mixing at the jet leading head, which is followed by an annular mixing layer that trails behind, connecting the leading vortex with the orifice rim. A successful deflagration is seen to develop for values of the orifice radius larger than a critical value, ac, of the order of the flame thickness of the planar deflagration, δL. Introduction of appropriate scales for the different flow variables provides the dimensionless formulation of the problem, with flame initiation characterized in terms of a critical Damköhler number ∆c = (ac/δL) 2 , whose parametric dependence is investigated. The numerical computations reveal that, while the jet Reynolds number exerts a limited influence on the criticality conditions, the effect of the reactant diffusivity on ignition is much more pronounced, with the value of ∆c increasing significantly with increasing Lewis numbers Le. The reactant diffusivity affects also the way ignition takes place, so that for reactants with Le > ∼ 1 the flame develops as a result of ignition in the annular mixing layer surrounding the developing jet stem, whereas for highly diffusive reactants with Lewis numbers sufficiently smaller than unity combustion is initiated in the mixed core formed around the starting vortex. Steady computations of weakly reactive subcritical jets are also employed to determine ∆c, giving results in close agreement with those of unsteady computations for Le > ∼ 1, when the role of the leading vortex is secondary. The boundary-layer problem that emerges in the limit of high jet Reynolds numbers is used to ascertain the effect of density variations and variable transport properties on the predicted critical Damköhler numbers, and to confirm the small influence of other dimensionless parameters such as the Zeldovich number, provided that its value is sufficiently large. The analysis provides increased understanding of deflagration initiation processes, including effects of differential diffusion, and points the need for further investigations incorporating detailed chemistry models for specific fuel-air mixtures.