The Brazilian, 22, upset Pistorius at the London Paralympics in 2012, winning the men's 200 metres (T44) by 0.07 seconds from the now-disgraced South African.
Pistorius was found guilty of culpable homicide for the death of girlfriend Reeva Steenkamp in September, and is awaiting sentencing in October.
Oliveira - a double-amputee like Pistorius - echoed the words of International Paralympic Committee communications boss Craig Spence, reiterating Pistorius was just one athlete in a wider movement.
"There is no negative effect on the Paralympic movement due to the Pistorius trial," Oliveira said.
"The movement does not depend on the image of one athlete. It's getting bigger and a personal problem from an athlete won't make a difference."
Oliveira said he feels like he needs to step up into the role filled by Pistorius - who often created headlines when he competed - especially given he would be next competing at an Olympics on home soil.
"I feel the pressure to be the new poster boy for the Paralympic movement," Oliveira said, with Pistorius facing up to 15 years in jail.
"It gets bigger because Rio will host the next Paralympics.
"As a Brazilian athlete during a Paralympic Games in Brazil, I have to give my best and to deal with the pressure from my friends, family and the Brazilian nation."
However, Oliveira claimed he would not back down from a Pistorius match-up should the latter be available.
"It would be great to have Pistorius at Rio 2016, competing against me," he said.
"He did a lot of good things for the Paralympic movement. I can face any rival at any competition."