A 3D direct numerical simulation (DNS) study of the evolution of a self-propagating interface in forced constant-density statistically stationary homogeneous isotropic turbulence was performed by solving Navier–Stokes and level-set equations under a wide range of conditions that cover various (from 0.1 to 2.0) ratios of the interface speed  $S_{L}$  to the r.m.s. turbulent velocity  $U^{\prime }$  and various (50, 100 and 200) turbulent Reynolds numbers $\mathit{Re}$ . By analysing computed data, the following issues were addressed: (i) dependence of the speed and thickness of the fully developed statistically planar mean front that envelops the interface on $U^{\prime }/S_{L}$ and $\mathit{Re}$ , (ii) dependence of the fully developed mean turbulent flux of a scalar $c$ that characterizes the state of the fluid ( $c=0$ and 1 ahead and behind the interface respectively) on $U^{\prime }/S_{L}$ and $\mathit{Re}$ , (iii) evolution of the mean front speed, its thickness, and the mean scalar flux during the front development after embedding a planar interface into the forced turbulence and (iv) relation between canonical and conditioned moments of the velocity, velocity gradient and pressure gradient fields.