TNT Chief Executive Nick Wells has said that the Royal Mail should stop "sabre-rattling."
Speaking on BBC Radio 4's World At One, he said: "They have just delivered record profits. Clearly TNT Post are trying to create innovation in the postal market. We are delivering choice for our customers, and that is good for the market overall, as well as creating jobs.
"It is very fair. We are an entrant in this market and we will pay Royal Mail, for the areas we don't cover, a very fair and reflective price.
Royal Mail should stop this sabre-rattling. We have a small market share, there is absolutely no threat to the universal service."
More top news
Star Wars actor John Boyega, Luther star Idris Elba and rapper Ice Cube are among 683 people who have been invited to join.
A gun shop in Chicargo is raffling off an AR-15 rifle to raise funds for victims of the Orlando nightclub massacre.
The partner of one of the 11 people killed in the Shoreham air crash said airshows have caused too many fatalities.