The first attempt last Friday was unsuccessful, he said, because they did not have the original copy of the child's birth certificate and a translation of Miss Shi's China passport, as required by the Health Sciences Authority.
So Cao arranged for the test to be done last Saturday at a private paternity testing company here.
"But (Miss Shi) backed out because she said she felt pressurised by the media attention," said Cao.
"She also feels a DNA test done here will not be accurate because I was the one who arranged for it and I was the one who appointed the lawyer."
He added he doesn't know when he'll be able to do the test as Miss Shi, 26, "is not picking up her phone" ever since she returned to Shanghai on Saturday afternoon.
Miss Shi had told Lianhe Zaobao in her first interview here that she is willing to let the girl take the DNA test.
Before she left, she told Lianhe Zaobao in another interview that she couldn't take the media attention and that she will be back to do the DNA test.
"I don't know what I'll do if she doesn't answer her phone... I want to be patient," Cao said.
"If she feels uncomfortable with (the DNA test), I don't want to force her."
He also told TNP: "I have my doubts about (the girl's) paternity."
So does he think it's a set-up?
"I don't want to think about this because it's very unhealthy," he replied.
Cao was advised by his lawyer not to address the claims made by Miss Shi in her interview with Lianhe Zaobao last Friday until the DNA result is out.
These include her claims that they had a one-night stand the night they met and that he had paid for her air ticket to come here in June 2010 and invited her to stay at his home for two weeks.
However, Cao told TNP he had met Miss Shi only three times, including last Friday, when he picked her and the girl up at their hotel to meet his lawyer.
There, Miss Shi had her rights explained to her through a translator, he said.
It was explained to her that if Cao is indeed the father, he has the responsibility to bring the child up until she's 21, he added.
"I made it known to her that I am willing to be responsible," Cao said.
On that day, before they met his lawyer, he was photographed feeding the girl a slice of cake at a cafe.
He said they spent around 10 minutes there and he wasn't in the right mood to play or chat with the girl.
When asked about his first impression of the girl, he said: "She's a lovely and healthy child. I thought she's really adorable."
Cao said he loves kids and dotes on his sister's children.
Miss Shi told the Chinese newspapers that she asked the child to call Cao "papa" when they met and that the girl did.
Cao sounded shocked when TNP told him of this.
He asked incredulously: "Do you think the child really recognised me (as her father) the first time she saw me?
"It was an orchestrated gesture. I won't react to this."
Cao also said he gave $2,000 to Miss Shi after she told him she needed money to return to China.