Both men deny charges of war crimes and crimes against humanity before the International Criminal Tribunal for the former Yugoslavia at The Hague, Netherlands.
Mladic said Tuesday testifying could prejudice his own case before the tribunal, the BBC reported.
The two exchanged greetings in their first public appearance together since the Bosnian war ended in the 1990s.
Karadzic, 68, faces 11 charges that include genocide relating to the Srebrenica massacre in July 1995.
Karadzic allegedly orchestrated the shelling of Sarajevo and the use of peacekeepers as human shields in May and June 1995. In Srebrenica, Bosnian Serb forces overran the U.N.-defended safe haven, slaughtering more than 7,500 Muslim men and boys.
Mladic was the general in charge of the troops.
During Tuesday's hearing, Karadzic's lawyer argued that Mladic was "the one person in the whole world who knows best what happened in the war in Bosnia."
Mladic, 71, at first refused to be sworn, saying: "Your subpoenas, your platitudes, your false indictments, I do not care one bit about any of it," the BBC said.
"I do not recognize this hate court," Mladic said. "It is a satanic court."
The judge later advised Mladic he wasn't obligated to answer questions if he thought his responses would incriminate him.
After answering the first question about his posts in the military, Mladic responded, "I refuse to testify on the grounds of my health and because it may prejudice my rights as an accused."
Mladic's lawyers said their client has a memory disorder that makes it difficult for him to distinguish between truth and falsehood, the BBC said. Karadzic read the rest of his questions and got the same reply.
The judge denied Mladic's two requests to read a seven-page statement and the session was adjourned.