The White House cleared the way yesterday for Texas International Airlines to acquire Continental Airlines, removing the last remaining government hurdle to the takeover.

In a decision announced by the White House last night, President Reagan said he had reviewed the proposed acquisition and saw no foreign relations or national defense reasons to disapprove it. The takeover had been approved unanimously by the Civil Aeronautics Board.

Under the law, the president could have disapproved the acquisition only on the basis of foreign relations or national defense considerations.

The president's decision ends a bitter eight-month battle fought out in a dozen different courts and governmental bodies across the continent.

Texas International, a Houston-based airline subsidiary of Texas Air Corp., already owns 50.3 percent of Continental's shares, purchased at a cost of more than $100 million. TI officials said last night they would begin anew their efforts to get representation on Continental's board of directors.

The takeover has been opposed strenuously by Continental officials and board members and an employes' association which had sought to thwart Texas International's takeover attempt by turning control of the company over to employes. The plan, which involved the issuance of new stock, was turned down by California officials.

Frank Lorenzo, president and chief executive officer of Texas Air Corp., last night referred to the battle and sought to reassure Continental's employes about the future of the company: "It is now time for the managements of both companies to direct our energies toward returning Continental to profitability.

"We realize that many Continental employes have grave doubts about this acquisition and that some employes have worked extremely hard and independently to defeat the acquisition," Lorezno said. "We want to reassure all Continental employes that our only goal is to build a strong and prosperous Continental, a task that will require trust, sacrifice and teamwork if it is to be achieved."

Since Texas International made its initial bid for Continental in February, the Los Angeles-based airline's financial situation has deteriorated significantly. At the height of the takeover battle last summer, Alvin Feldman, the airline's president, committed suicide.

A spokesman for Continental said the airline was "deeply disappointed in President Reagan's decision," but the "next moves" are up to Texas International.

"The days ahead are still uncertainm but Continental is dedicated to continuing its financial-recovery program and presumes that it also the desire of its majority shareholder, Texas International."

The White House statement on the merger said the president was aware that many had expressed concern about future levels of air service to the Pacific Islands, especially the Trust Territory of Micronesia, now served by Continental and its subsidiary. But the board's decision approving the acquisition includes safeguards designed to prevent unilateral reduction of air service to the islands, the president added, and "additional safeguards" can be developed by the agencies to assure the continuation of adequate air service.