One of the conditions for the adoption of the Su-7B fighter in 1961 was a requirement for Sukhoi to develop an all-weather variant capable of precision airstrikes. Preliminary studies of the C-28 and C-32 aircraft showed that the basic Su-7 design was too small to accommodate all the avionics needed for the mission.OKB-794 (later known as Leninets) was tasked with developing an advanced navigation/attack system, codenamed "Puma", which was to form the core of the new aircraft. That same year, the United States' proposal for its new all-weather strike fighter was called TFX. The resulting F-111 was to feature variable-geometry wings to significantly increase payload, range, and low-altitude penetration capabilities.

In 1962–63, Sukhoi initially intended to build an aircraft without the F-111's movable-wing complexities. He designed and built a mock-up of the S-6, a delta-wing aircraft powered by two Tumansky R-21 turbojets and a crew of two in tandem. The mock-up was inspected, but no further work was ordered due to lack of progress on the Puma equipment.

In 1964, Sukhoi began work on the S-58M. The aircraft was to be a modified version of the Su-15 interceptor (factory designation S-58). Meanwhile, revised Soviet Air Force requirements called for a low-altitude strike aircraft with short takeoff and landing capabilities. A key feature was the ability to cruise supersonic at low altitude for extended periods to penetrate enemy air defenses. To achieve this, the design included two Tumansky R-27 afterburning turbojet engines for cruising flight and four Rybinsk RD-36-35 turbojet engines for short takeoff and landing. Side-by-side crew placement was implemented because the large antennas of the Orion radar required a large frontal cross-section. To test the six-engine configuration, the first Su-15 prototype was converted into the S-58VD flying laboratory, which was operated from 1966 to 1969.