Texas International Airlines said yesterday it will fight Pan American World Airways for control of National Airlines.

In TXI's first public statement on Pan Am's proposed merger plans with National - which followed TXI's takeover bid by more than a month - TXI indicated it would not back down in the David-and Goliath battle.

"We believe - although we cannot make any predictions - that the Civil Aeronautics Board will approve TXI's acquisition of control of National and will disapprove a merger of National and Pan Am," Frank Lorenzo, TXI's president, said yesterday.

In a complaint filed with the CAB yesterday, the Houston-based carrier also charged that Pan Am already has gained "unlawful control" of National by virtue of the stock interest it holds and its influence over National in bring the Florida-based carrier into a definitive merger agreement last week.

Under the Federal Aviation Act, prior CAB approval is required for transactions that would result in the control of an airline. Although TXI concedes that Pan Am's 4.8 percent stock interest in National alone might not create a control relationship - TXI itself holds 20.1 percent of National's common stock - it argued yesterday that Pan Am's dealings with National culminating in the signing of a merger agreement have established a "very active control relationship between the two companies."

TXI noted that the agreement calls for a vote of National's shareholders on the proposed Pan Am merger in the next two or three months, long before the CAB will reach its final decision on which merger proposal - if any - to approve. For the shareholders vote, National's management will be trying to convince National shareholders to vote for the Pan Am and, "in effect, against the TXI acquisition," the complaint states.

"This is particularly significant," TXI contended. "This is an active, positive step by Pan Am and National acting in concert, or by Pan AM acting through National's management toward effectively solidifying Pan Am's control relationship with National and toward eliminating a competing bidder for control of National - Texas International," the complaint said. "Clearly, Pan Am is now in active control of National and it is exercising that control."

TXI also contended that a Pan Am-National merger may violate the Clayton Antitrust Law by substantially lessening competition in air travel from the East Coast to Europe.

William T. Seawell, Pan Am's chairman and chief executive officer, said he had not seen a copy of the TXI complaint. "We are confident, however, that our actions with regard to National have been completely legal," Seawell said.

"Meanwhile, we are moving forward with our plans with National and are holding meetings with [them] to work out further merger details," he said.

Both airlines seeking control of National have been required by the CAB to place any National stock they acquire in a trust that is supposed to insulate each airline from any control over National while the merger applications went through the CAB's administrative hearing process.

So far, TXI has disclosed purchases of 1,718,300 shares of National stock for $47.8 million, including brokerage commissions, for an average price of $27.83 a share. Under Pan Am's agreement with National, Pan Am would pay $41 for each National share.

In yesterday's trading, Pan Am's stock was off 5/8 to 10, National's stock was up 1 to 37 1/4 and Texas International was unchanged at 15 7/8.