Martensitic transformation induced by the matrix-precipitate interface (or other internal surfaces) for single and two martensitic variants is studied using a thermodynamically consistent multiphase phase field approach. Three order parameters are considered; two of them describe the austenite (A) ↔ martensite (M) and variant Mi ↔variant Mj transformations in a matrix, and the third one describes the finite width matrix - non-transforming precipitate interface. The energy of the matrix-precipitate interface reduces during A→M phase transformation from the value for energy of A-precipitate interface, γA, to value for energy of M-precipitate interface, γM, due to its dependence on the order parameter related to the austenite↔martensite transformation. Such an interface increases the temperature for barrierless martensite nucleation well above the critical temperature for A→M transformation. The nucleation temperatures strongly depend on the ratio Δ¯ of the widths of the matrix-precipitates interface and A−M interface. New “phase diagram” for transformation temperatures between austenite, martensite, and premartensite versus Δ¯ has been presented for neglected mechanics for two cases when magnitude of Δγ=γM−γA is larger than the energy of the A−M interface (0.2 N/m). For Δγ=−0.5 N/m, below a critical width ratio Δ¯*, a layer of premartensite appears jump-like within the matrix-precipitate interface and progresses with reducing temperature, until it loses its stability and jump-like transforms to complete martensite in the entire matrix. However, for Δ¯≥Δ¯*, the entire matrix transforms to martensite without any premartensite. For Δγ=−0.3 N/m, no premartensite appears and the A matrix completely transforms into M at lower temperatures that the case with Δγ=−0.5 N/m. The combined effect of the energy of the matrix-precipitate interface, Δ¯, precipitation-induced misfit strains, and applied displacements on the boundary of the sample on nucleation of martensite and complex microstructure evolution in the systems with a single and two martensitic variant(s) is studied. Obtained results are important for controlling cyclic martensitic transformations in shape memory and elastocaloric alloys and designing alloys with desired characteristics of martensitic transformations.