The Defense Department plans to begin construction next year on what could become its first Strategic Defense Initiative weapon, a $400 million ground-based laser, according to information given Congress early this month.

The free-electron laser, being developed by Lawrence Livermore National Laboratory in California, has often been described as the most promising technology for President Reagan's "Star Wars" defense program by its director, Lt. Gen. James A. Abrahamson.

Abrahamson has also said recent breakthroughs in mirror technology will permit sending laser beams through Earth atmosphere and into space where they could destroy Soviet missile boosters or satellites.

Construction at White Sands, N.M., is expected to take three to four years, according to congressional sources.

It is the first step toward an experiment, planned for the early 1990s, in which the laser's beam will be directed from White Sands to a mirror in space and reflected back to destroy a missile penetrating the atmosphere minutes after its launch.

Many problems must be overcome before this "uplink" experiment can take place, according to sources inside and outside of the government. For that reason, some critics of the SDI program have said starting construction of the White Sands facility is premature.

John Steinbrunner, director of national security programs for the Brookings Institution, yesterday called building the laser facility "advanced mischief."

"Long before it fits into a ballistic-missile defense" and after the space mirror is positioned, he said, the laser will cause controversy because it and the mirror could have varied uses, even to "start fires on the ground" in other parts of the world.

When completed, the White Sands laser alone would also be capable of serving as an antisatellite weapon, beaming directly into space where it could burn through or blind satellites as they pass over U.S. territory.

Since White Sands is an approved test site under the 1972 Antiballistic Missile Treaty, the planned laser would not violate that treaty when used as a test device. Sources expressed disagreement on whether it would violate the treaty when used with a mirror as a missile-defense weapon.

The Soviets have ground-based lasers in use at their test site near Sary Shagan in the south-central U.S.S.R., but they are less powerful than the proposed free-electron laser, according to intelligence sources.

CIA officials, however, have told Congress that the Soviets are capable of deploying a ground-based, antisatellite laser by the 1990s.

Limited as the Soviet lasers are, the United States once protested to Moscow about use of one to "blind" a U.S. satellite, according to informed sources.

Although the SDI organization wants to start construction of the facility next year, the experimental version of the Livermore laser has yet to achieve the performance level needed to be a successful weapon.

To meet the expected standards, the laser would have to be 10 to 100 times more powerful than today's biggest laser, according to John Pike, a Federation of American Scientists expert on the SDI. The mirrors, he said yesterday, would have to be three to four times the diameter of today's largest mirror.

Part of the SDI construction program calls for building a temporary facility for the full-scale laser at Livermore. It would be moved later to White Sands as the permanent facility progresses.

The SDI organization is studying a $250 million proposal from one company to build the primary laser-director mirror on the ground, according to informed sources. Two types of space-based mirrors are under development, they said.

The entire system is expected to cost about $1 billion.