Virgin says it has very few slots at Heathrow
Sir Richard Branson has called on the US government to refuse British Airways permission to agree ticket schedules and prices with American Airlines.
It is one year since British Airways applied to regulators for anti-trust immunity, which would in effect allow it to dominate Heathrow Airport.
BA says Sir Richard wants the "global aviation regulatory system to be applied solely in his interests".
The BA decision is seen as a key test for future US competition policy.
It is already difficult to compete with BA at Heathrow, Steve Ridgway, chief executive of Virgin Atlantic, told the BBC.
"We don't have plenty of slots, we have been at Heathrow now for almost 20 years and we still have less than 3% of slots at Heathrow, so we are still a minnow in that sense, " said Mr Ridgway.
"You go there and you maybe see quite a few Virgin planes, but we are not able to compete effectively.
"We try very hard and I think we have done a very good job but if this is allowed to happen, if BA and American are allowed to come together, to put the sort of dominance they have on those key routes like New York and Boston and Miami and so on, then the regulators just need to be on their guard," he added.
But in a statement, BA said that it was confident that regulators would agree and dismissed Sir Richard's concerns.
"He wants the regulators to give the Virgin group anti-trust immunity to collaborate with another airline to fly across the Pacific, but claims it would be 'anti-competitive' for British Airways to be given the same approval for collaboration with another airline across the Atlantic," it said.
The BA deal with American Airlines would offer customers greater choice, it said.
"Virgin Atlantic is concerned about the BA/AA deal because it feels it can't compete," said Saj Ahmad, an airline analyst.
"In fact, the US Govt has little grounds to stop this deal given the amount of previous alliances it has approved in the past."
He added: "Also with the Open Skies pact in place, competition has gone up, not down. It is also ironic that Virgin continues to lobby against this deal given its silence on other, bigger deals that have previously been approved."
Airlines across the world have been hit by the global slowdown.
In May, Virgin Atlantic reported a sharp rise in profits in the year to the end of February, bucking the trend seen by other airlines.
Annual pre-tax profits reached £68.4m ($109m) - helped by a rise in premium fare passengers - nearly double the £34.8m seen in the year earlier.
The results are in contrast to other airlines, including British Airways, which reported an annual loss before tax of £401m last week.