He denied lying to the Chinese evening papers on Friday when reporters called him to ask about Miss Shi and her claim.
Cao was reported as saying that there's no such thing, even though he had met Miss Shi and the girl just hours earlier.
He said: "I was driving when the call came in and I shouldn't be giving interviews when I'm driving.
"I said (to the reporter) that I haven't read the newspaper and so I shouldn't comment until I've seen the report."
He said his family and friends are supportive throughout this period, and MediaCorp has also been helpful.
He will continue with his work as usual and will go to Malaysia next month to film a Chinese drama.
Cao said he does not know how this will affect his career or his reputation and does not want to think too much about it.
He also said: "My friends are as curious as I am (about this paternity case).
"She came to Singapore with her claims and she tapped on the media and raised a storm. And now she left without doing a DNA test.
"How do you expect us to react? People are also asking why she didn't come to Singapore when she was pregnant. Why wait 19 months?
"I have due respect for the decisions she made in the past.
"I only have one simple (request) now: show me the DNA."