Sir Philip Green, chairman of retailer Arcadia, has written to Labour MP Frank Field, suggesting a call for a truce over what he considers to be a personal attack.
Mr Field, chairman of the Work & Pensions select committee, wrote to Sir Philip last month regarding concerns about the future of Arcadia pension scheme members.
Following reports of a potential sale of Arcadia to a Chinese conglomerate, Mr Field asked Sir Philip if he would apply for regulatory clearance before any transaction, as well as publish the details of the application.
In his reply, the business tycoon denied that he is in talks to sell his business, which comprises brands such as Topshop, Evans and Dorothy Perkins, to Shandong Ruyi.
Regarding Mr Field's concerns about Arcadia's pension scheme, Sir Philip said there is a recovery programme in place of £50m a year, and if the company is sold, "there are pension obligations and there is a process that they will need to adhere to should that arise".
Sir Philip said: "I think in future it would be good manners if, when you send a letter, you would give time to respond without giving it to the press 15 minutes later.
"I am aware, as everyone else is, how you love your press profile on the back of me. I do think however the time has come for this to stop."
Both men have clashed in the past over the failure of BHS, with Sir Philip accusing Mr Field of making a personal attack and using him as "political football".
The Pensions Regulator has been investigating the case since.
In the end, a £363m settlement with Sir Philip was reached to fund a new independent pension scheme for 19,000 former BHS workers.
The new scheme would pay members the same starting pension that they were originally promised by BHS, with greater ongoing benefits than they would have received from the Pension Protection Fund.
Sir Philip concluded: "Mr Field, why don't we call a truce? You say it is not personal, it could not be more personal.
"Go and tackle Carillion or someone else. I think 18 months later everyone is bored with this story."