When President Reagan authorized the secret sale of U.S. weapons to Iran, administration officials hired Southern Air Transport Inc., a Miami-based air cargo firm, to fly the arms overseas.

The operation was so secret that Southern Air says its employes were told not to discuss the flights with anyone and were required to sign secrecy oaths.

Now, the Federal Aviation Administration has ordered Southern Air to pay a $50,000 fine for failing to obtain approval from the Department of Transportation to fly such hazardous material overseas.

DOT has refused to give the airline permission to fly other hazardous cargo overseas for private clients while the issue of the fine, which Southern Air is contesting, is pending.

Contending it is the "innocent victim" of secrecy imposed by the White House, Southern Air filed suit in U.S. District Court here late last month asking the court to order transportation officials to lift the ban preventing the firm from flying commercial hazardous cargo overseas.

Southern Air argues in its legal papers that it is unfair and a violation of due process procedures for transportation officials to hold up approval of future commercial hazardous cargo flights while the company is fighting the FAA fine.

"This policy is, essentially, a blacklisting of {Southern Air} to force {it} to pay a civil penalty . . . ," Southern Air says in the court papers.

A Transportation Department spokesman yesterday declined to comment, citing the pending lawsuit.

David M. Kirstein, a lawyer for Southern Air, said yesterday that company officials are incensed by the actions of the FAA and transportation officials. "Our client feels that the whole thing is kind of nutty that they should be treated this way," Kirstein said.

He said that Southern Air officials were assured that their participation in the Iran operation was legal and that all the necessary authorizations for the flights had been obtained.

"They knew they were doing this at the direction of the White House and the National Security Council," Kirstein said. "It's like we're being penalized for assisting the government in this operation. Whatever you think of the {Iran arms sales} it does not seem appropriate . . . to punish us."

Southern Air president William G. Langton said in an affidavit filed with the lawsuit that, at a January 1986 meeting in Washington, Southern Air was asked to participate in the flights by retired Air Force major general Richard V. Secord, who was working with then-NSC aide Oliver L. North on the secret Iran and contra initiatives.

Southern Air also assisted Lt. Col. North's private network in providing maintenance and other services for a clandestine air resupply operation North and Secord set up to fly arms to the contras.

Langton said he agreed to fly the weapons involved in the Iran arms sales after he was assured that "all the necessary governmental authorizations" were obtained.

He said the arrangement called for Southern Air to fly TOW antitank missiles from Kelly Air Force Base in San Antonio to Israel on company planes. He said Southern Air crews then flew the missiles to Iran aboard foreign-owned planes that congressional testimony showed belong to the Israeli government. He said the company flew three TOW shipments in this manner, two in February 1986 and one in May 1986.

Allan Horowitz, an FAA attorney involved in the case, said yesterday that the FAA's position is that Southern Air has been in the business of transporting hazardous material for many years and knew that permission to fly such cargo must be obtained from the Transportation Department. Horowitz said the burden is on Southern Air officials to obtain the necessary approval regardless of what they were told by Secord, who, he added, was not a government official.

Kirstein said that before each flight Southern Air officials were given a Defense Department form that is the same authorization the company receives when it flies under a separate contract hazardous material overseas for the U.S. military.

However, Horowitz said, the Defense Department document Southern Air claims it received does not provide permission for flights to foreign-controlled airports, which is where the Iranian missiles were flown.Staff writer Nancy Lewis contributed to this report.