In 1995, in the midst of Budyonnovsk hospital hostage crisis, Rybakov, together with the State Duma Sergei Kovalev and Viktor Kurochkin, on behalf of Prime Minister Viktor Chernomyrdin negotiated with Shamil Basayev, who seized the hospital. The talks failed to agree on the release of most hostages - to ensure the safety of terrorists along with them on the buses back to Chechnya, only 140 volunteers were to go, including negotiators. In the village of Zandag, Rybakov was released along with the other hostages.