Several hundred protesters gathered in Lafayette Park north of the White House yesterday to call for shutdown of existing nuclear power plants and a ban on construction of new nuclear generating stations.

"What happened at Three Mile Island could happen at any nuclear power plant," Peter Franchot, a staff attorney for the Union of Concerned Scientists told the midafternoon rally. "We were duped about the safety of nuclear power plants and the cost of nuclear power plants."

The Lafayette Park protest was among numerous demonstrations across the United States over the weekend, prompted by the accident late last month at the Three Mile Island nuclear power plant near Harrisburg, Pa. One demonstration took place yesterday on the steps of the State Capitol in Harrisburg.

The rally in Lafayette Park was sponsored by the Potmac Alliance, an antinuclear group active in Maryland, Virginia and the District of Columbia. The alliance is pressing for a shutdown of nuclear plants for safety inspections, a moratorium on additional nuclear stations and a shift from nuclear power projects to development of solar energy and other non-nuclear conservation measures.

The Potomac Alliance plans a march today from Lafayette Park to the Capitol with stops at government and private nuclear agencies and firms.

At yesterday's rally, speakers denounced both nuclear power plants and nuclear weapons. They contended that nuclear plants pose severe occupational hazards and asserted that low-level radiation emitted by nuclear stations endangers human health. They criticized the Carter administration's energy policies and charged that many nuclear accidents have gone largely unreported.

"The incident in Harrisburg was not the first and it certainly won't be the last of the partial meltdowns. Think of it as a sneak preview," said Michio Kaku, a physics professor at the City College of New York. Kaku cited four previous-though less serious-incidents in the United States and England since 1955.

Antiwar activist Philip F. Berrigan urged the demonstrators to "struggle against the war-makers like the one across the street." Lafayette Park is across Pennsylvania Avenue from the White House.

Despite the somber tone of the speeches, yesterday's rally took place in a leisurely atmosphere on a chilly, largely overcast afternoon. The demonstrators, many of them high school and college students who were sprawled on the park grass, listened to folk and rock music, watched antinuclear skits and occasionally broke into chants of "no nukes."

Their placards included "Hell No, We Won't Glow," "We All Live in Harrisburg" and "Melt Down Corporate Power." At the northern edge of the park, members of the Anacostia Energy Alliance assembled solar collectors and built an improvised solar-powered water heater. U.S. Park Police estimated the crowd at about 500 persons.

On the Capitol steps in Harrisburg yesterday, demonstrators staged what they described as the "last rites" for Three Mile Island, contending that the nuclear plant should be buried.

"They say only two or three people will die of cancer because of what happened," Dr. Geoffrey Corson, chief surgeon at Harrisburg's Polyclinic Hospital, told the Associated Press. "If it were someone I loved, I wouldn't feel it was a fair exchange."

Antinuclear demonstrations also took place over the weekend in San Francisco, Groton, Conn,; Seattle, Los Angeles, Phoenix, Bloomington, Ind.; Ithaca, N.Y.; Brooksville, Fla. and Lancaster, Pa. CAPTION: Picture, Judi Bari, Lafayette Park demonstrator, with a new twist to an old slogan. By Douglas Chevalier-The Washington Post