To understand what went on inside the KGB and the Kremlin, for as far as we can determine, it is important to keep in mind the broader developments in the Cold War and the role of Cold War intelligence.

Back in the USSR, Khrushchev's foreign policy was quickly unravelling and the Kennedy assassination would further cement that sense of failure. Every initiative of Khrushchev had failed to produce results at best, and brought the world to the brink of war at the worst of times. Khrushchev was running out of time, and would indeed be removed from his position in 1964, with the Politburo citing the Cuban Missile Crisis as the main reason for his removal.

During the Cuban Missile Crisis, Soviet intelligence had a mixed record. On one hand, it was embarrassed by the fact that the US had penetrated the GRU, with moles providing them information on Soviet deployment plans on Cuba. The punishment was the appointment of a KGB officer, Pyotr Ivashutin, to lead the military GRU. On the other hand, the GRU was part of the crisis' peaceful solution, establishing a secret backchannel for negotiations between Khrushchev and Kennedy.

The KGB meanwhile, had since the late 1950's already noticed Lee Harvey Oswald, who had come to the USSR because of his communist sympathies but eventually returned to the US. Once back in the US, he came on the radar of the FBI as a potential Soviet agent, but he was in fact turned down by the KGB after he offered his services. Oswald was an unstable person, and did not exactly make a great candidate for clandestine work, given his openly communist leanings. The FBI concluded the same thing; the KGB would never recruit such a figure.

When Oswald finally did kill Kennedy, Khrushchev was about to launch his final bid to achieve a breakthrough in his relations with the US, and had actually again intended the GRU to establish a secret backchannel. Kennedy's death destroyed these hopes, and Khrushchev saw it as an American Rightist conspiracy to escalate the Cold War.

The KGB quickly realized it could get the blame because press stories began to circulate in the ensuing days that Oswald had been in the Soviet Union. "We began receiving nearly frantic cables from KGB headquarters in Moscow, ordering us to do everything possible to dispel the notion that the Soviet Union was somehow behind the assassination," a former KGB officer stationed in New York wrote. "Lubyanka [KGB] told us to report the simple facts: that Oswald had lived in Minsk, that he had never been trusted and was suspected of being a CIA agent, that he had been kept under surveillance, and that he left the Soviet Union and returned to America on his own, without KGB help." The KGB officer described the mood in the Kremlin, based on incoming cables, as "rattled".

The KGB, searching for information that confirmed this view, cited Polish intelligence sources that Texan oil tycoons had paid Oswald to kill Kennedy so that the Soviets would get the blame. It may have also been an attempt by the KGB to avoid the Kremlin's punishment for having become involved with a loose cannon like Oswald in the first place.

In the subsequent years, especially as the US government still investigated whether Oswald had acted alone, the KGB's disinformation service mobilized its assets to disseminate conspiracy theories about the Kennedy assassination, and propagate the Kremlin's version of events.

Based on archival leaks in the 1990's, the Soviet story of Oswald's stay there can be largely confirmed. Fat files were kept of him, as they virtually watched all of Oswald's moves, suspecting him of ties to the CIA.

After the US published its official report on the Kennedy assassination in 1964, the KGB was relieved it had come to the same conclusion that Oswald had acted alone. Spreading conspiracy theories carried on well into the 1970's however, as it was now a useful theme to exploit for political warfare.