President Carter yesterday signed a Civil Aeronautics Board order formally approving a revised package of airline routes that significantly expands U.S. air service to Europe.

Nonstop air service is authorized to Europe from 11 new American cities and three airlines - Northwest Airlines, Delta Air Lines, and Braniff Airways - are premitted to fly across the Atlantic for the first time.

The order includes the President's controversial decision to award Braniff, rather than Pan American World Airways, a new route between Dallas and London - a route Braniff said yesterday it would begin serving on March 1.

In December, the President said he would approve most to the board's route and carrier selection proposals stemming out of its four-year transatlantic route proceeding except in two respects: he wanted to give Braniff instead of Pan Am the Dallas-London route, and he wanted to add Amsterdam and Frankfurt to the European route awards of National Airlines.

Although Carter said he based his decision on his "foreign policy" of encouraging competition in international aviation, some charged that politics - namely, the influence of Texas congressmen and Robert Strauss, the President's special trade ambassador - influenced his decision. The White House denied the charges.

Whatever the reasons, his rejection of the board's decision made CAB Chairman Alfred E. Kahn angry enough to have considered resigning, at least "fleetingly," he said. Kahn told reporters the next day he was "not pleased" with the president's decision, which he said made a mockery of the board's lengthy and time-consuming process aimed at arriving at reasoned decisions.

He complained that the President gave no adequate explanation for his decision and never mentined the work the board went through to arrive at it's decision. " . . . We are no less dedicated than the President to promoting competition in international aviation markets," Kahn said.

Along with signing the order, the President sent Kahn a note thanking the board for "the cooperative spirit" it demonstrated in revising its order as he directed on an expedited basis. Then he added: "Although I disagreed with a portion of the board's decision, I believe that you and I are both attempting by decisions such as these to achieve the same goal - a more competi-tive environment for the international aviation industry."

Under the provisions of the board's order the President accepted. Delta was awarded a new route between Atlanta and London; National got new routes from New Orleans, Miami and Tampa to Paris; and Northwest got the right to fly between nine cities, including Washington/Baltimore, and Glasgow and points in Denmark, Norway, Sweden, Finland and Iceland.

In addition, most of the Pan Am's exsiting authority was nenewed, and nonstop Miami-Madrid authority was added, in addition to a Houston-London route it is able to start in three years.

Also, Trans World Airlines' existing authority was renewed and it was given permission to serve Pittsburgh, Denver, St. Louis, Cleveland, Minneapolis/St. Paul, and Kansas City direct to Europe. A spokesman for TWA said yesterday the airline has no definite plans to institute any of the newly authorized service.