The clip comes just a week after his Melodifestivalen co-presenter Gina Dirawi received strong criticism after publishing a picture of an anti-semitic book on her blog.
Reacting to the video, which appeared on Tuesday in the tabloid Aftonbladet, Danny Saucedo said his comment was "a damn clumsy choice of words".
"Anyone who knows me or has met me knows that I am not racist. I myself am foreign", he added.
Peter Nyrén at Swedish Television's (SVT) programming unit said the incidents may damage people's trust in the public broadcaster, but said he did not think next year's song contest will be affected.
"We have had direct discussions with these two people to ensure that they embrace the fundamental values one has to hold as a presenter at SVT, meaning a belief in equality and democracy," Nyrén told Swedish Radio.