A potpourri of protesters in New York

New York was a city under siege on Saturday. An estimated three-quarters of a million poured into the city for the march and rally against nuclear arms .

And many left with the belief that their presence had made a powerful statement against the worldwide nuclear arms buildup.

Carla Oden of San Francisco said, ''Before I came to this rally, I thought it was hopeless - that nuclear holocaust was inevitable - but after seeing the support today, I have hope that we can save ourselves.''

Marjorie Carr organized a train-load of 180 people from Montauk, New York. She said, ''I believe that our only hope is for the US to take the initiative and at least try to freeze nuclear weapons.''

But reactions were as diverse as the individuals present. One marcher expressed concern over whether the Soviet Union will ever listen to popular call for disarmament. Many became bored or dissatisfied with several stridently anti-Reagan speeches and left.

Still, the anti-nuclear movement counted the day as a victory. As Carlos Santiago of Washington D.C. said: ''The only way things will change is for this to become a mass movement. Today's rally was a beginning of that movement.''

The demonstrators assembled north of the United Nations Plaza and proceeded through midtown Manhattan to Central Park. Many wore buttons (''Ban the Bomb''), tags (''We made history on June 12''), or one of thousands of multi-colored origami (folded paper) necklaces in the shape of a crane, brought by the contingent from Hiroshima.

Marchers from Australia, Japan, Denmark, and Sweden shouted protest phrases. Hundreds from Quebec chanted, ''Nucleaire, no merci.'' Eighteen of this group bicycled from Montreal. One of the cyclists called it ''Well worth it, the march is wonderful.''

Sixty members of the Japanese Federation of Youth, one of the numerous groups from Japan, marched in the protest. Yoshaki Kanda, a coordinator, said ''I hope our voices are heard by President Reagan and Mr. Brezhnev to stop nuclear arms build-up.''

Order was maintained throughout the protest. New York Police Captain Frank Biehler said it ''was a great crowd, and as far as I know, the rally was without incident.''