Research into the breakup of continents and formation of ocean basins has advanced in recent years, with deep-marine seismic data providing much of the impetus for new concepts. Attention has been focused on nonvolcanic (magma poor) margins; meanwhile, a satisfactory explanation for volcanic (magmatic) margins with their distinctive seaward-dipping reflectors (SDRs) has been missing. SDRs are composed of subaerial lava flows of tholeiitic basalt erupted during the transition from continental rifting to seafloor spreading, when the crust is both stretched and constructed from asthenosphere-derived magma. Here we present remarkable seismic images down to 40 km offshore East Greenland, showing that a newly described type of extensional fault plays an integral part in the ascent of magma and the building of transitional crust. Two such faults define an axial horst block supported by rising magma where the plates separate. Lava collects in seaward-growing half graben on either side of the horst, while new gabbroic crust is accreted along the flanks of the magma chamber in dilational shear zones beneath where the faults detach. Ultimately, rising asthenosphere reaches the base of the magma chamber, causing the horst to split, thereby initiating seafloor spreading. The model we describe shows how extension and magmatism interact at the boundaries of rifting plates.