In August, Holder's Justice Department sued to stop U.S. Airways and American Airlines from merging saying the merger would result in less competition and higher airfares for customers.
It adds that passengers flying in and out of Washington, D.C., would be "particularly hurt," since the combined company would own 69 percent of all slots at Reagan Washington National Airport.
In his letter, Burgess rejected the idea that the two airlines compete on most routes.
"There are nearly 900 domestic routes that American Airlines and U.S. Airways fly and only 12 of them overlap," he wrote. "Further, American Airlines flies to 48 cities not served by U.S. Airways, and U.S. Airways flies to 64 that American Airlines does not serve."
Burgess also said the suit appears to be an effort by the administration to attack this merger after it left other airline mergers alone.
"The baseless claims by DOJ give rise to a peculiar and arbitrary challenge to this merger," he wrote. "It seems the DOJ is trying to remedy past mistakes when it did not challenge former mergers by punishing American Airlines and U.S. Airways for its previous inaction."