Pan American World Airways said yesterday it has made an unsolicited offer to purchase besieged National Airlines.

After a nearly seven-hour National board of directors meeting in Miami yesterday, National Chairman L. B. Maytag, who has been fighting a takeover attempt by Texas International Airlines, said National would consider the Pan Am proposal.

Under Pan Am's proposal, offered National by Pan Am Chairman and Chief Executive Officer William T. Seawell on Tuesday, Pan Am would pay National shareholders $35 in cash for each share of National stock. Trading of National stock was halted all day yesterday at the company's request, pending a news announcement at the end of yesterday's board meeting. National's stock closed Tuesday at 30 1/4.

Yesterday, Maytag said the company will study regulatory, financial and other questions, and would analyze the offer from the point of view of the shareholders, before deciding whether to accept it. He said the company also would meet further with Pan Am's representatives to clarify details of its proposal.

A merger of the two companies would make the combination the second largest U.S. carrier behind United Airlines. Using total operating revenues in 1976, Pan Am is the fifth largest airline and National is the eleventh.

A merger would also given Pan Am long-sought domestic routes. Seawell said yesterday he considered the nature of Pan Am's and National's operations generally, and their route structures in particular, to be "highly complimentary" so that a combination of the two would offer "substantial advantage" to shareholders, employees of both companies, the cities served, and the public.

Besides being subject to the negotiation of a definitive agreement and approval of both corporations and possibly lenders, the merger is subject to the approval of the Civil Aeronautics Board and the President, neither reassured.

In hearings before the Senate Commerce Committee earlier yesterday in fact, CAB Chairman Alfred E. Kahn had talked about the considerable questions about merger proposals that had already been made.

In the present situation of the industry where entry is not yet free . . . I think it is reasonable to put a heavy burden of proof - not an insurmountable one - on carriers who wish to diminish the number of existing carriers," he said.

"At the same time" he added, "I do fully recognize that individual mergers may make competition more effective rather than less, and we do have to be open to the demonstration that . . . these losses of competition are offset by efficiency advantages, by putting together more powerful competitors, aggressive competitors and the like.

Although Pan Am spokesman talk in terms of meshing two different put complimentary systems in a merger, the CAB might more likely see the companies as two very serious potential competitors, board sources say. One source noted that National has been seeking an expanding international role that the CAB has been sympathetic toward in which it would be competiting with Pan Am, that Pan Am is an applicant for Miami-California routes that National currently flies, and that Pan Am is seeking to make Houston a hub for its proposed domestic route system which would make it a direct National competitor.

[Although Pan Am has not yet received domestic route authority from the board, Kahn told Congress yesterday that a provision in a proposed bill encouraging the CAB to give domestic route authority was unnecessary since it was going to. Although an administrative law judge grants World Airways the authority to offer low-fare transcontinental service in an initial decision released yesterday, it is considered very likely that the board would also give Pan Am that authority when it reviews the case.]

Pan Am said it would file an application with the CBA today seeking approval of the proposed merger along with a request that it be given the authority to acquire additional shares of National pending approval of the merger.

In its quest to take over National Texas International initially purchased a 9.2 percent share of National and last week won the tentative approval of the CBA to buy and put additional shares up to 25 percent in a trust with certain conditions.

Yesterday, a lawyer for Texas International said TXI had purchased an additional 225,800 shares which gives it about an 11.9 percent share of National's stock.