Papers released by Pistorius' family Monday indicated the attorneys reiterated their arguments at the bail hearing, saying he is not a flight risk and should be allowed to travel outside South Africa with official permission, the BBC reported.
In setting bail at $110,000, the judge ordered the athlete to surrender his passport, avoid his home in Pretoria where the killing occurred and report to a police station every Monday and Friday.
In their appeal, Pistorius' lawyers said the bail conditions were "unwarranted and not substantiated by the facts."
Pistorius is charged with killing his girlfriend, Reeva Steenkamp, 29, by shooting her through a closed bathroom door in his home Feb. 14. Pistorius said he thought she was a burglar when he fired multiple shots through the door.
A family friend told the BBC Pistorius could be "on the verge of suicide" and was forced to sell his race horses to pay for his legal costs.
Mike Azzie, who has been in contract with Pistorius, said the athlete often talks about Steenkamp and her family.
"He has no confidence in his tone of voice and he is almost like someone that is walking around in circles and doesn't know where he is going," Azzie said in a documentary to air Tuesday. "I would say that, just speaking to him, he is a broken man."
"I would go as far as to say that he could be on the verge of suicide," Azzie said. "It really worries me."
Pistorius was released on bail Feb. 22 and is due back in court in June.