He said that he feels "strongly" about Lata's allegations as his father "has never been involved in a controversy before this".
An old feud came back to the limelight when Lata claimed in an interview to a leading daily that she had refused to sing with Rafi and had only agreed when Rafi had sent an apology letter to her. The interview was published Tuesday.
Shahid called a special press conference here Wednesday to give his verdict on Lata's claim.
"My father was a national property. His fan following is bigger than any artist. If she can prove that my father had written an apology letter to her, then she should come out and produce it. In case she does, I am ready to apologise to her," Shahid told reporters here.
"I think she (Lata) is insecure of my father's fan following and that is why she has done this," he added.
Mohammad Rafi was one of the most popular singers of 1950s and 1960s and gave hits like "Chaudhvin ka chand ho", "Husnwale tera jawab nahin", "Chhoo lene do nazuk hothon ko" and "Maine poocha chand se". He died in 1980. He was 55.
He also sang duets with Lata such as "Yunhi tum mujhse baat karti ho" and "Tujhe jeewan ki dor se".
Shahid also claimed that his father had no competition at the time, whereas Lata did.
"There is no competition between her and my father as actors like Shammi Kapoor and Dharamendra wanted him to sing for them. But there were other female singers like Suman Kalyanpur, Hemlata and Mubarak Begum and others who might have been competition to her. So maybe her career was at stake," he said.
Did he try to get in touch with the singer?
"I have not tried to call her regarding this as she has never responded to my calls before. She always seems to be busy whenever I have called her in the past," Shahid said.
He also added that he was being supported by others in the industry as well, but refused to take any names.