The House yesterday adopted, after heated debate, a controversial amendment that would make it easier for the federal government to override a state's objections to its selection as the permanent burial site for the nation's high-level radioactive waste.

On a 190-to-184 roll-call vote, the House eliminated a provision in the nuclear waste bill that would have allowed a state to veto its selection for a permanent waste repository, and would have permitted that veto to be overridden only by a vote of both houses of Congress.

The new provision, sponsored by Rep. James T. Broyhill (R-N.C.), would still permit a state to veto its selection. But the veto would not be binding on the federal government unless one house of Congress voted to sustain the state's veto. A nuclear waste bill already enacted by the Senate contains a similar clause.

Broyhill, in arguing for the amendment, contended that when the lengthy process set up for selecting a site for the first nuclear waste repository culminates in a decision by the president in 1987, "a governor's veto could just halt the project in its tracks" if a two-house override were required.

"I think that's going too far," he argued.

"I am a firm believer in state's rights," agreed Rep. William E. Dannemeyer (R-Calif.), "but this is an issue of national significance. It transcends state's rights. The issue is whether we in this country, who run the country's affairs, are to have the means to dispose of high-level waste. Somebody has to decide."

But Rep. James D. Santini (D-Nev.), whose state is certain to be a leading candidate to become the permanent repository, termed Broyhill's approach "a fraud and a sham," and argued that requiring the designated state to get a house of Congress to back its veto "wipes out any meaningful state role."

"When a state is picked as the site, the other states are going to be ganged up against it," concurred Rep. G.V. Montgomery (D-Miss.), whose state also is regarded as a leading contender. "It's just not fair."

The clear concern of the half-dozen states that have locations regarded as potential sites for a permament nuclear waste repository was apparent earlier when Rep. Trent Lott (R-Miss.), the minority whip, pressed an amendment that would disqualify from consideration locations containing 1,000 or more people per square mile.

Opponents of this amendment accused Lott of proposing his formulation in an effort to make it virtually impossible for the federal government to select Mississippi's Richton Salt Dome as a site for the repository. Lott's amendment was defeated 296 to 8l.

The outlook for ultimate House passage of nuclear waste legislation was significantly strengthened when an amendment by Rep. Morris K. Udall (D-Ariz.), which would make it more difficult for the government to build a facility for monitored retrieval storage of nuclear waste pending final burial, was adopted by a voice vote.

A number of supporters of nuclear waste legislation have opposed construction of a temporary monitored retrieval storage facility, fearing it might be used as a way of circumventing the stiff environmental and licensing requirements that will be imposed on a permanent repository.

The amendment offered by Udall, however, eases some of these concerns by requiring the preparation of full environmental reports if such a temporary facility is to be built, and requiring that the facility be subject to licensing by the Nuclear Regulatory Commission.

The House is scheduled to resume debate on the nuclear waste legislation on Thursday, when a number of additional amendments remain to be offered.