The Soviet Union has offered to expand and extend its 12-year agreement with the United States on a joint research program to harness fusion power released in a controlled thermonuclear reaction, the process that triggers explosion of a hydrogen bomb, administration sources said.

The Soviets suggested that the agreement be extended 30 years and expanded to require that the two countries spend as much as $3.5 billion to build a reactor demonstrating that electricity could be safely and commercially produced by fusion, the sources said.

If the United States agrees, no decision on the demonstration plant's location would be necessary for at least 15 years because of the amount of work to be done.

The Energy Department would not comment on the Soviet offer yesterday, and the State Department would say only that it is one item "under consideration" at the Geneva meeting of President Reagan and Soviet leader Mikhail Gorbachev.

The sources said the two departments are understood to look favorably on the Soviet offer. The Defense Department has historically opposed any fusion agreement with the Soviets.

In 1973, the two nations agreed to exchange fusion-research findings.

An Energy Department official, who asked not to be identified, said the DOE considers the fusion pact "the most open and fruitful agreement" it has ever had with the Soviet Union. There has been little urgency about the pact since world oil prices began to fall from their all-time highs in the spring of 1981.

Each nation has had a fusion-research program for 20 years, but progress toward a working model of fusion power has been slow and expensive.

The United States has built what the Tokomak Fusion Test Reactor at Princeton University for $314 million, and the facility is expected to begin operation in 1987.

One version of the Tokomak has demonstrated fusion temperatures of almost 100 million degrees but has not reached the "break-even point," at which the fusion machine generates as much electricity as it consumes to sustain such high temperatures.

The next step for the Tokomak is to demonstrate that the point can be reached.

The Princton machine is named after the Russian word for doughnut and is shaped like one, a configuration that the Soviets demonstrated 20 years ago as the best way to contain fusion temperatures.

The Soviets have pursued the same approach but, according to administration sources, are thought to lag behind the United States after once leading.

The Defense Department has opposed working with the Soviets on fusion research, partly because much of the U.S. work involves high-energy laser beams that could be used as space weapons or to enrich uranium for nuclear weapons.

Extensive U.S. research programs in laser fusion are under way, and the United States has plans to use a laser method to enrich uranium for civilian nuclear-power plants and atomic weapons.

The Energy and State departments have said this country will not perform laser-fusion research with the Soviets if the 12-year pact is extended and expanded.

The Tokomak fusion machine works through "magnetic containment" and has nothing to do with lasers.

If the Tokomak test reactor at Princeton demonstrates that a break-even point is attainable, the next step in demonstrating commercial fusion power is to build a bigger machine that will sustain 100-million-degree temperatures longer.

If that step is achieved, an engineering model of a commercial prototype would be attempted -- something the Soviets are thought to have offered in suggesting that the agreement be expanded.

An engineering model would cost at least $1 billion and take 10 years to build.