Royal Mail shares at one point yesterday fell 10 per cent on the fears but one rival, TNT Post UK, called on the newly-privatised company to "stop whinging".
The row erupted as Royal Mail posted its first set of results since its controversial £3.3 billion stock market flotation in October, seeing profits rise to £430 million in the year to March 30, up from £403m, on the back of increased parcel revenues.
As the universal service provider, Royal Mail is required to provide access to competitors such as TNT for "final mile" deliveries.
Moya Greene, its Chief Executive, called for "timely regulatory action" to prevent the impact of direct delivery competition from undermining the economics of the universal service.
"TNT Post UK can cherry-pick easy-to-serve urban areas, delivering easy-to-handle post to homes less frequently than Royal Mail."
But Nick Wells, TNT Chief Executive, urged Royal Mail to stop its "sabre rattling".
He said: "We are delivering choice for our customers and that is good for the market overall.
"We are an entrant in this market and will pay Royal Mail [a fair price] for the areas we don't cover."
Ofcom, the industry regulator, said it kept the market under review and did not believe there was "a threat to the sustainability of the universal postal service".