American--Soviet negotiations for a total ban on tests of nuclear explosives will be expanded to include Britain in talks starting in Geneva on July 13, it was announced yesterday.

Another U.S. delegation headed for Moscow to begin talks Wednesday on another of President Carter's goals, "complete demilitarization" of the Indian Ocean. Officially, these discussions have a more modest title, "arms limitation in the Indian Ocean."

Paul C. Warnke, director of the U.S. Arms Control and Disarmament Agency, is leading the American delegation for the Indian Ocean discussions, after heading U.S. negotiators in last week's nuclear test ban talks here.

Carter administration sources cite these negotiations, and others, as evidence that the Moscow-Washington clash over human rights in the Soviet Union is not freezing up progress on other issues.

U.S. officials said "progress was made" in the American-Soviet nuclear test ban discussions last week, conducted in tight secrecy. To some officials, this signifies that prospects are increasing for moving toward a goal of many years' standing, a complete ban on nuclear testing, through what is known as a Comprehensive Test Ban Treaty. Others say the progress is only on negotiating procedure.

A treaty of this kind would seal off underground nuclear testing, excluded from the 1963 treaty originated by the United States, the Soviet Union and Britain to prohibit nuclear tests in the atmosphere, under water or in outer space. Since then, the United States and the Soviet Union simply transferred their testing underground, where they continued to develop new weapons.

There continues to be uncertainty on the American side, some sources concede, about whether the current Soviet objective is to seal off all nuclear testing, or to gain political ammunition against its chief Marxist ideological rival, China.

China has not signed the 1963 partial test ban. The Soviet Union often has said it will agree to a total ban only if it applies to all nuclear weapons states, especially China.

To try to surmount that obstacle, President Carter said in his first press conference, in February, that the United States and the Soviet Union should first demonstrate they can stop the nuclear arms buildup, make "substantial reductions" in their arms levels, and then ask other nations like China and France to join in.

The President also said "we could negotiate" with the Soviet Union on specific exceptions to the test ban, to meet the Soviet demand for nuclear explosions for peaceful uses, such as diverting the course of a river.

At present there is a U.S.-Soviet treaty draft before Congress to permit "peaceful nuclear explosions" under specified controls, and a companion treaty draft to ban all nuclear weapons explosions larger than 50 kilotons, the equivalent of 50,000 tons of TNT. A total test ban presumably would overtake both of these pending treaties.

The new test ban negotiations, and the impending Indian Ocean talks, are among the side-products of the U.S.-Soviet nuclear strategic arms limitation talks (SALT) in Moscow last March. Those SALT talks, which deadlocked, resumed in Geneva.

Nations bordering, or near, the Indian Ocean, have opposed U.S.-Soviet military competition in that region, military including development of the American-British installation on the island of Diego Garcia.

Australian Prime Minister J. MalColm Fraser, who begins an official visit to Washington today, is expected to discuss the Indian Ocean in his talks here, a State Department spokesman said yesterday.