In an Instagram post, Preetipls, whose real name is Preeti Nair, and her brother Subhas, said: "We're sorry for any hurt that was unintentionally caused. Behind the music video is an initiative to provide greater consciousness to consumers, corporations, and the many faces of Singapore," Channel News Asia reported.
The siblings also said that the message behind the music video was "that opportunities must be for everyone".
In the NETS E-Pay ad, Chinese personality Dennis Chew appeared in "brownface" - the act of darkening one's fair skin to mimic that of another race - as an Indian character and as a Malay woman wearing a headscarf.
It also showed him cross-dressing as a Chinese woman.
The three-minute video by the siblings, posted on social media on Monday, criticised the ad for its stereotypical portrayals of the different races in Singapore.
The video was laced with profanity, targeting the Chinese.
Police on Tuesday said it was investigating the video for "offensive content" after a report was lodged against it.
The electronic payment service provider also issued an apology earlier this week where it said that the intent of the campaign was to "communicate that e-payment is for everyone", and apologised for "any hurt that its campaign had caused".
Ministers and religious leaders weighed in to criticise the video, with Law and Home Affairs Minister K. Shanmugam saying that a line has to be drawn on videos that "attack another race".
( With inputs from IANS )