Mukhamedjanov declined to say what the new evidence was but said it indicates the investigation into Sarsenbaev's murder is proceeding successfully.
Mukhamedjanov said he would share the new evidence with the country's media soon.
Sarsenbaev's body was found last month outside Almaty. His bodyguard and driver were also killed. The head of the Senate's administration, Erzhan Utembaev, and five security officers were arrested for the killings.