Mr Rudd was due to attend an inter-faith religious dialogue with local Labor MP Tony Zappia on Wednesday.
That is the same day Ms Gillard and her cabinet will fly into Adelaide to host a community event.
Mr Rudd has told Sky News he decided to reschedule his visit to avoid any controversy.
"I don't think anyone would've known I'd be doing this but it's now been splashed all over the front page of the Sunday Adelaide newspapers," he said.
"I don't want any controversy for Tony Zappia. I don't want any controversy which would detract from the important work the PM and her team will be doing in Adelaide that day."
Mr Rudd says his goal is to help Labor candidates to election victory.
"My objective is to do whatever I can on the ground in support of local Labor candidates and local Labor members to get them re-elected in order for the Gillard Government to be re-elected at the next election.
"That's what I do."
Mr Rudd also said it is time the leadership debate was placed into "cryogenic storage".
Earlier this month Mr Rudd reaffirmed his loyalty to Ms Gillard amid reports there is growing support within Caucus for a potential comeback.
The former prime minister also attracted attention last week after making a thinly veiled criticism of Treasurer Wayne Swan following and the mining tax.
But he says he has no intention of challenging Ms Gillard for the leadership.
"A couple of weeks ago I said everyone should take a cold shower, last Friday I said they should have an ice bath," he said.
"It's time this debate was put into cryogenic storage. Frankly, it ain't happening."