"I believe her role in the Agency's use of torture and efforts to destroy evidence of it was neither minor nor incidental," the release said.
The senator pointed out that the nominee, who is currently serving as CIA Deputy Director, personally wrote a cable directing the agency to destroy the interrogation videotapes.
Kaine said he backed Republican Senator John McCain in expressing dissatisfaction in Haspel's inability to denounce torture.
Earlier this week, US Senator John McCain refused to vote to confirm Gina Haspel's nomination, saying that she was unfit to run the CIA, citing her "disturbing role in overseeing the use of torture by Americans.
Haspel, who currently serves as acting CIA director, oversaw the interrogation of a detainee at a secret US prison in Thailand who was waterboarded 83 times in a single month. She also reportedly participated in the destruction of videos of interrogations that have since been characterized as torture and outlawed by Congress.