President Carter's military response to the Soviet combat brigade in Cuba is a series of limited show-the-flag exercises.

Marines will land in Guantanamo to display U.S. resolve to keep using that base in the heart of Cuba, and Navy ships will ply the Caribbean under the command of a new headquarters in Key West, Fla.

After about two weeks, the Marines will leave Guantanamo and then be followed by others in a series of landings to dramatize the American commitment to the base and capability to reinforce it.

But those are the only immediate and visible military actions the president will take to underline his commitment to combat any Soviet adventurism in the Western Hemisphere.

For the longer term, Carter has ordered the Pentagon to step up the planning for a quick reaction force of soldiers and Marines that could fly to world trouble spots.

In dusting off a Kennedy administration plan that Congress disapproved in the 1960s, a senior defense official said last night that equipment for those troops would be kept overseas on ships in friendly ports. These new floating storehouses will be conventional cargo ships manned by civilian crews or perhaps Navy reservists.

Also, the Pentagon officials said, the Air Force will be given money to buy an additional four DC 10 flying tankers for aerial refueling, to make it easier to transport quick-reaction troops to distant points.

Those steps go only a short distance toward remedying what military leaders have been decrying as a critical shortage of ships and aircraft for long-distance lift of troops and weaponry.

The senior defense official, who could not be identified under the ground rules of the briefing given to reporters at the Pentagon last night, said it has not been decided whether the additional money for the cargo ships and flying tankers would come from a request to Congress this year for additional money or be financed out of next year's defense budget.

The Marine landings on Guantanamo, the official said, would start in about two weeks and involve about 1,500 Marines and 2,000 sailors aboard amphibious ships. No aircraft carrier will accompany the task force, he said.

The officials said that the Marines will probably "practice an assault," adding that this used to be standard training procedure at Guantanamo until a few years ago.

One purpose is to practice reinforcing Guantanamo, he said. The presumed goal is to impress Cuban President Fidel Castro, but this was not mentioned in the Pentagon briefing.

Currently, there are 420 Marines and 1,850 Navy personnel on Guantanamo. The Marines' primary task is guarding the $100 million base while most of the sailors there train crews of ships that stop at Guantanamo and then conduct drills in the Caribbean.

While the defense official acknowledged last night that one purpose of the Marine landings would be to "show determination," he refused to put the new command at Key West in the same category.

Instead, said the official, the command of from 60 to 100 people representing all the services is designed to provide a sharper focus on the whole Caribbean area.

The headquarters at the Navy air station now in caretaker status at Key West would enable the Pentagon to respond faster to developments in the Caribbean, the official said.

However, ships exercising in the Caribbean will still be under the command of Atlantic fleet headquarters in Norfolk.

One task force of 16 Navy ships already is in the Caribbean for a 12-day exercise that Navy officials said was planned before the flap erupted over the Soviet presence in Cuba. Other exercises stemming from Carter's determination to be more aggressive in showing the flag in the Caribbean are scheduled to follow.

Carter in his speech last night said "we will monitor the status of the Soviet forces by increased surveillance of Cuba."

Asked last night if that meant U.S. planes would resume flying over Cuba, the senior defense official said this decision has not yet been made.

U.S. reconnaissance planes will step up their monitoring of the island from the international airspace on Cuba's perimeter, the official said. The administration may resume overflights if needs for additional information appear urgent, he said.

President Carter suspended overflights of Cuba by Air Force SR71 Blackbird spy planes as a goodwill gesture to Castro. He resumed them only briefly last November to take pictures of the Soviet Mig23 fighter planes delivered to Cuba.

The United States also will intensify satellite surveillance of Cuba and interception of both voice and signal communications.

While all of these military steps outlined by administration officials avoid any direct confrontation with the Soviet Union, Carter served notice on Moscow last night that he would not tolerate any "Soviet unit in Cuba" moving against "the United States or any other nation in this hemisphere."

The president said last night that "American intelligence obtained persuasive evidence" that some Soviet forces had been organized into a combat unit. This was a step down from the original State Department assertion that the evidence of the combat force was "unambiguous."

The defense official briefing reporters said the Joint Chiefs of Staff endorsed the military measures announced by the president last night. "I don't recall they recommended anything we're not doing," he added.

The chiefs do not consider the 3,000 Soviet combat troops a threat to the United States or Caribbean countries, partly because the Soviets have not sent transport planes and ships to Cuba.

The bigger threat, in the chiefs' view, is the Cuban expeditionary forces that are creating turmoil in the Third World and could compromise U.S. interests in the Persian Gulf.