The United States, as part of its drive for greater military impact is the troubled Middle East and Southwest Asia region, may use Egyptian air bases for future operations, Carter administration officials said yesterday.

The potential role for the Egyptian facilities was disclosed in the wake of the announcement Tuesday that joint training exercises have been conducted recently to test the ability of U.S. planes to operate from the bases.

According to the officials, the exercises in Egypt are one step in an evolving U.S. attempt to respond to the crises in Iran and Afghanistan by establishing the potential for effective use of military force to protect the security of states in the area.

The extreme sensitivity and secrecy surrounding this effort were underscored by the manner in which State Department spokesman Hodding Carter responded to questions about the U.S. - Egyptian exercises.

He put his principal emphasis on a declaration that the administration has decided to reject offers from both Egypt and Israel to establish permanent U.S. bases in their countries.

In addition, he insisted that the exercises in Egypt, which involved the most advanced U.S. electronic surveillance planes, do not mean the United States is planning any military operations aimed at trying to free the Americans held hostage in the U.S. emmbassy in Iran.

In private, though, several administration officials went beyond the spokesman's public statements to admit, that the United States is exploring a number of possible ways to make use of facilities in the region to deploy military forces quickly and effectively if the need should arise.

That goal was sketched in a nonspecific way by President Carter yesterday in the first of a series of briefings for prominent Americans about the situations in Iran and Afghanistan.

A White House official said Carter, at a breakfast with diplomatic and defense officials of previous administrations, said that the substantially increased U.S. military presence in the region "would have to be maintained at a higher level."

Although the president did not go into details, the administration officials said a key, long-range aspect of this effort to project U.S. power in the area involves the search for storage and service facilities for American ships and planes.

Exploratory talks and studies are under way with Kenya, Somalia and Oman about possible regular U.S. use of their air and naval facilities. The officials said the joint exercises with Egypt -- the first by the two countries -- represented an exploration of the feasibility of using facilities on the other side of the vast region stretching from the Indian Ocean to the Mediterranean.

They described as a "one-shot deal" the operation involving two AWACS planes, used to spot incoming aircraft and surface ships, and a supporting force of abuout 250 American personnel.

Future use of Egyptian facilities, the officials said, will depend on the situations that arise in the region and whether the bases would lend themselves to any American operations mounted in response.

The main initial purposes, the officials continued, were to demonstrate the capacity for military operations in the area, to enable American personnel to become familiar with using the facilities and working with Egyptian forces, and to establish a precedent for future use of the Egyptian bases.

For the time being, the offficials said, the main U.S. emphasis will be on seeking cooperative arrangements with friendly countries of the region to use their facilities rather than set up new bases under U.S. control. That, the officials stressed, is because many states in the region, like Saudi Arabia, while desiring a better U.S. ability to offer them protection, do not want the political tensions that might be caused by putting American bases in their backyards.

It was for similar reasons that the administration decided against accepting Israel's offer to use bases there, the officials said. Such a move, they noted, would increase the risk of anti-American feeling in a region dominated by Islamic states hostile to Israel.

The officials said Secretary of State Cyrus R. Vance is expected to meet shortly with Agha Shahi, senior foreign policy adviser to Pakistan President Mohammad Zia ul-Haq, to discuss resumption of U.S. aid to that country on the borders of Afghanistan and Iran..

Although strengthening Pakistan's defenses is a key part of the administration's projected response to the Soviet invasion of Afghanistan. State Department spokesman Carter cautioned: "What we are not doing is going about the area seeking formal treaty alliances or the imposition of some new form of Pax Americans."