The Abbott government proposed removing the words insult, offend and humiliate from section 18C of the Racial Discrimination Act in March.
Concerns have been raised over the proposed changes, announced by Attorney-General George Brandis, which would see the stipulations in 18C replaced with provisions outlawing racial vilification and intimidation.
Addressing the media on Tuesday, Mr Abbott said the plans were “off the table”.
Mr Abbott described the move as a "leadership call".
"When it comes to counter terrorism, everyone needs to be part of team Australia," he said.
"The government's proposals to change 18C of the Racial Discrimination Act have become a complication in that respect. I don't want to do anything that puts our national unity at risk at this time, so those proposals are now off the table."
Mr Abbott said he discussed the matter with the cabinet on Tuesday.
Opposition Leader Bill Shorten said he was "deeply concerned" that Mr Abbott used the announcement of new anti-terror measures as a cover to dump the changes.
"As late as last night, the Attorney-General was defending the changes of the government to 18C," he said.
"... Between last night and today, the Attorney-General of Australia has been rolled by his cabinet. George Brandis has been humiliated by his colleagues."
Mr Shorten also used the announcement to continue pressure on the Coalition to backdown on its budget measures.
"This embarrassing backdown has been forced on a prime minister who did not want to announce what he's announced today," he said.
"I predict that this will not be the only backdown the prime minister will make in the coming days."
Human Rights Commissioner Tim Wilson has taken to Twitter to express his disappointment in the move.
Opposition MPs have welcomed the announcement, while News Limited columnist Andrew Bolt has also weighed in on his blog.
"Too many lobby groups hate free speech," he said.
"And the reforms were badly sold. I suspect the country will be poorer for this."
Bolt was involved in one of the most high profile cases involving section 18C.
A complaint was lodged against himself and the Herald & Weekly Times in 2011, which alleged that Mr Bolt had discriminated against light-skinned Aboriginal people.
The Federal Court of Australia ruled that the columnist and the newspaper had acted unlawfully, finding that some Aboriginal persons who have a fairer skin were reasonably likely to have been offended, insulted, humiliated or intimidated by the published comment.
