"I have always been one of your greatest admirers and supporters," Tata has written to Singh who responded by saying that those in public life "inevitably face" criticism and it should be used constructively to guide the government.
Tata, who will step down on December 28 to take over as Chairman Emeritus of Tata Sons, has conveyed to Singh his "sense of shock at reading the completely untrue, sensationalised headlines and reporting of a recent interview" to the Financial Times of London.
In his letter dated December 10, he referred to his press statement issued on December 8 and said he had clarified that "I have neither 'lashed into the Prime Minister', 'rapped India' nor 'warned government of inaction'."
Enclosing transcript of the interview to show he never criticised the Prime Minister, Tata has told Singh, "I have always been one of your greatest admirers and supporters, publicly and privately."
"I have valued your trust and confidence at all times and I was very deeply aggrieved to have a publication of the repute of Financial Times of London misrepresent the comments of my interview with them and be the cause of any misunderstanding between you and me."
Contending that the last thing he would want is a "misunderstanding between us created by an opportunistic journalist relecting his personal views and that of his newspaper, Tata said, "I can only apologise for any embarrassment that this media misrepresentation may have caused you or the government."
Thanking Tata for his "kind words and support" expressed in the letter, Singh responded on December 12, "I have always believed that those in public life should be able to make constructive use of the criticism that they inevitably face about some of their actions."
"Even as such criticism should persuade us to introspect about the path we are following, it is our conviction that should necessarily guide us forward."