British Midland (BMI) has called on the government to try to broker a deal for an "open sky" policy for air traffic between the EU and the US.
Current regulations limit the number of carriers which can operate on routes across the Atlantic.
At present, British Airways and Virgin Atlantic have a monopoly on flights to the US from Heathrow.
BMI chairman Sir Michael Bishop said an agreement should be reached by June to avoid damaging delays.
The deal to break the monopoly of airlines currently flying to America from Heathrow would lower ticket prices and increase passenger choice, supporters of the deal argue.
UK-US negotiations on the regulations have been going on for years, but Sir Michael, speaking from Washington, said that current negotiations "appear more positive than any time in the last three years".
He said that the American side had moved significantly from its initial position, and that the EU appeared motivated to bring about competition, but argued that obstacles were being posed by the airlines which are currently benefiting from the monopoly.
"We stand on the verge of a landmark agreement," he said.
"Yet that agreement risks being derailed by a series of red herring issues which appear to be driven by the needs of BA and Virgin".
He called on Transport Secretary Alistair Darling and EU commissioner Loyola de Palacio to push for the negotiating parts to come to a final agreement.