An ambitious program to spend $20 billion constructing a pilot nuclear fusion power plant by the year 2000 received final approval from the House yesterday and went to the White House. President Carter is expected to sign it in the next few days.

Rep. Mike McCormack (D-Wash.), who sponsored the measure and has long pushed for such a program, said he was 'absolutely elated."

The commitment to harness fusion energy, the kind that fuels the sun and is used in the hydrogen bomb, will be "an Apollo-like program, but considerably more important, and more difficult because we're exploring new technology," McCormack said.

The Apollo program to put a man on the moon was simpler than achieving fusion, according to both critics and supporters of yesterday's action, because of the difficulty of producing, sustaining and then containing temperatures equal to the sun's: 100 million degrees.

"Most scientists now believe we have the physics under control. We have only the question of the materials of the first [containment] wall left to work out," McCormack said.

But fusion would solve the world's electricity problem forever since the main fuels for it would be isotopes of hydrogen that can be extracted from sea water. McCormack said. Scientists have been working on it for the past 30 years.

The new law authorizes the Department of Energy to increase its current $394 million appropriation by 25 percent each year until $1 billion is reached in 1987 totaling $20 billion by the turn of the century. The engineering work is to be done by a Center for Fusion Engineering, located at an existing major research center, where a test facility will be built by 1990.

If feasibility sutdies warrant, construction will then proceed on a full-scale prototype fsion power generating plant to be operational 10 years later. There has been no decision on where such a plant would be located.

A test facility at Princeton University is now under construction and is widely expected to demonstrate the fusion process for the first time in about 1983.