We report on the fabrication by Au-assisted molecular beam epitaxy of InP nanowires with embedded InAsP insertions. The growth temperature affects the nucleation on the nanowire lateral surface. It is therefore possible to grow the wires in two steps: to fabricate an axial heterostructure (at 420 degrees C), and then cover it by a shell (at 390 degrees C). The InAsP alloy composition could be varied between InAs0.35P0.65 and InAs0.5P0.5 by changing the As to P flux ratio. When a shell is present, the InAsP segments show strong room-temperature photoluminescence with a peak wavelength tunable from 1.2 to 1.55 mum by adjusting the As content. If the axial heterostructure has no shell, luminescence intensity is drastically reduced. Low-temperature microphotoluminescence performed on isolated single wires shows narrow peaks with a line width as small as 120 microeV.