Texas International Airlines yesterday dropped its quest for control of National Airlines, leaving Pan American World Airways' proposed merger with the Miami-based airline almost certain.

Although there are still some hurdles, yesterday's action virtually assures Pan Am of acquiring the domestic routes it has long sought to supplement its international routes, as well as a fleet of 55 airplanes at a fraction of their cost in today's market.

Texas International stepped aside yesterday by agreeing to sell to Pan Am for $50 a share the 2.1 million shares of National it has acquired during the last year. The price per share is the same Pan Am has agreed to pay all National shareholders under the merger plan. Under an agreement reached yesterday, Pan Am will buy 790,700 of the shares within the next few days and will pick up the remaining shares later, assuming its merger is approved. In addition, Pan Am agreed to pay Texas international an additional $3 million now to get the agreement.

Pan Am already holds 51.4 percent of National's stock; adding the 24.5 percent Texas International holds will give the carrier 75.9 percent of the outstanding National common stock.

Although the Pan Am-National combination is still subject to final Civil Aeronautics Board and White House approval, it is considered unlikely that the proposed merger would be turned down. The CAB had already tentatively approved the competing bids of Pan Am and Texas International for control of National.

While Eastern Airlines is also seeking to merge with National, its chances for CAB clearance are rated slim because the two carriers' route systems overlap on numerous cities. Eastern holds just 100 shares of National stock.

"I consider the agreement advantageous for both air carriers," William T. Seawell, chairman of Pan Am, said yesterday after the deal was worked out. Frank Lorenzo, chairman of Texas International, said he believed the agreement was in the best interests of TI, its employes and stockholders. Since the CAB had given preliminary approval to the Pan Am-National merger, which had also been approved by National's shareholders, "further pursuit of our acquisition efforts would not be in our best interests," he said.

Lorenzo had stunned the airline industry and Wall Street last July when the Houston-based airline picked up 9.2 percent of the stock of National, an airline three times its size, thus starting the scramble for control. Having paid an average price per share of $28.20 for all its National stock. Texas International stands to make before-tax profits of about $45 million from its year-long venture.

Texas International officials declined comment on rumors that they might use the proceeds to buy stock in Continental Airlines which, like National at the time Texas International began to buy its stock, has an asset value well in excess of the price of its stock. "The money's going in the bank," is all one Texas International official would say yesterday.

There was heavy trading in the stock of Continental this week, leading to speculation that it might be a possible takeover target since its proposed merger with Western Airlines was tentatively rejected by the CAB.