Pressure has been building on front-running presidential candidate and Davao City Mayor Rodrigo Duterte since he made a joke in connection with the rape and murder of an Australian missionary during a 1989 hostage crisis in Davao City during a campaign rally on April 12.
"I apologize to the Filipino people for my recent remarks in a rally. There was no intention of disrespecting our women and those who have been victims of this horrible crime," read the statement.
"Don't force the issue because I will never really apologize," he said, according to a CNN Philippines translation of his comments.
He said he knew nothing about the statement of apology released by his party, and said the offensive remarks had been uttered in a burst of anger at the criminals.
'Let it bring me down'
"I was angry she was raped, yes that was one thing. But she was so beautiful, I think the mayor should have been first. What a waste," he said, according to a CNN Philippines translation of the comments, which appeared in a YouTube video over the weekend.
Despite the widespread condemnation, Duterte has repeatedly defended the remarks, saying Monday night that it was simply how people like him, who were not born rich, spoke, according to CNN Philippines.
"If it brings me down, let it bring me down. If it brings me up to the presidency, then well and good. I will serve you, but I will not as a matter of honor apologize for (it)," he told reporters.
Australia: Don't trivialize rape, murder
The Australian embassy in the country was critical of his comments on Facebook: "Rape and murder should never be joked about or trivialized."
Jejomar Binay, current vice president and presidential candidate, said that Duterte didn't deserve to be elected to the country's top job.
"Rape and murder of a woman is not funny at all. Mister Duterte, don't you have a mother? Don't you have daughters? Your statement is simply revolting."
CNN's Kristie Lu Stout contributed to this report.