Energy Secretary John S. Herrington announced yesterday that the administration would halt the search for a high-level nuclear waste repository in an eastern state, saying a single repository in a western state "will be adequate in the foreseeable future."

The announcement came hours after President Reagan formally approved three sites in western states as final candidates for the nation's first high-level radioactive waste disposal facility. Those sites -- Yucca Mountain, Nev.; Deaf Smith County, Tex., and Hanford, Wash. -- will undergo detailed investigation before the Energy Department recommends one to the president in 1994, as required by law.

Nevada immediately filed suit against the plan, and officials in Texas and Washington state said they also intended to challenge the selections.

The abrupt decision to abandon the search for a second site in the East drew a chorus of cheers from officials in seven eastern states, including Virginia, that were selected as preliminary candidates. The other states were Georgia, Maine, Minnesota, Wisconsin, North Carolina and New Hampshire.

"It virtually ensures that no nuclear waste disposal site will be located in Virginia," said Sen. Paul S. Trible Jr. (R-Va.). "I'm pleased that the Department of Energy has recognized that a second disposal site would be unwise, unnecessary and expensive."

Environmentalists, however, charged that the decision was driven by politics, and warned that the search for a second site could be resurrected as quickly as it was killed.

"This was absolutely a political decision," said Brooks Yeager of the Sierra Club. "How could George Bush campaign in New Hampshire two years from now when the citizens are rioting in the streets? This decision offers little comfort to the states affected."

Opposition to the prospect of a nuclear dump has been intense in all of those states, particularly in Maine and New Hampshire, where it has become a heated political issue.

Herrington denied that politics played any part in the decision, which he said stemmed from budgetary constraints and reduced estimates of the amount of nuclear waste the nation will generate in the next several decades.

"It is the department's opinion that the nation need not consider a second repository until at least the mid-1990s -- or much later," Herrington said. "It is clear that to go ahead and spend hundreds of millions of dollars on site identification now would be both premature and unsound fiscal management."

That is the reverse of what Ben C. Rusche, head of DOE's Civilian Radioactive Waste Management office, told a congressional panel last month. In testimony before a House Energy and Commerce subcommittee April 23, Rusche said the department had determined that a second repository was needed and the selection process should continue.

According to an administration official close to the selection process, the department changed its position to minimize controversy while it pursues the initial disposal site in the West. "Our major concern is the first repository," he said. "There is not a clear need yet for the second repository and it has generated a lot of controversy and pressure."

Three years ago, Congress ordered DOE to prepare plans for two permanent underground repositories for highly radioactive waste from nuclear power reactors and weapons production facilities. The repositories, essentially huge vaults more than 4,000 feet below ground, must be capable of storing the waste safely for up to 100,000 years.

When western states protested that they should not be required to store waste for the entire nation, Congress stipulated that the first site would be limited to 70,000 tons of waste. DOE is also trying to get congressional authorization for a temporary waste depot in Tennessee.