The sponsor of the demonstration was the June 12 Rally Committee, an umbrella organization of religious and secular peace groups. The groups participating ranged from radicals seeking immediate unilateral disarmament by the United States to moderates asking a resumption of negotiations on arms cutbacks.

The rally was to mark the United Nations Second Special Session on Disarmament, which began last Tuesday. Many world leaders are to give addresses at the session, including President Reagan on Thursday.

Many of the dozens of speakers during the day urged the participants to continue the movement when they returned to their homes. ''We shall not suffer silently the threat of nuclear holocaust,'' said City Council President Carol Bellamy, who addressed the crowd near the United Nations.

Because of the crush, the rally in the park ended an hour later than its scheduled 6 P.M. close. Outside the area of march and rally, the city was strangely quiet for a Saturday afternoon. The police, who had 5,000 officers on overtime, had warned motorists to stay away from Manhattan because of traffic jams. Businesses complained that the rally had cost them millions of dollars.

The demonstrators had massed in blocks between First and Third Avenues from 47th to 56th Streets for the morning speeches in the Dag Hammarskjold Plaza and the march across 42d Street, up Fifth and Seventh Avenues and on to the Great Lawn at 81st Street. In the assembly areas, diverse groups were thrust together. On one street, the marching units, in order, were the Communist Party U.S.A., the Kings County Democratic Coalition and Animators Against Armageddon, a cartoonists' group.

Along the march there were floats and balloons, jugglers and babies in strollers. Many artists had prepared antinuclear events in the last month and had brought their creations to the march. There were dancers and scientists, computer programmers and environmental activists, religious groups of all denominations.

Perhaps the only dissenters in the huge throng were a group of about 40 people who stood for a time at 42d Street and First Avenue. They carried signs saying, ''Build Up or Freeze to Death'' and ''Peace Is a Soviet Weapon of Conquest.'' Leonard Holihan, a businessman based in London, said his organization was called Coalition for Peace Through Security. Profusion of Placards