Leaders of antidraft groups are meeting in Washington this weekend to organize local demonstrations across the country to protest government prosecution of young men who fail to register for the draft.

Spokesmen for the groups, which included the national Committee Against Registration and the Draft (CARD), Black Veterans for Social Justice and the Women's International League for Peace and Freedom, said yesterday the demonstrations would take place late this month and in August. They also said they are exploring ways of raising money to defend men accused of failing to register.

William G. Smith, a California lawyer who is national cochairman of CARD, chided the government for trying "to scare everybody to register for the draft by prosecuting a few vocal opponents." He said, "These young men going to court will not be martyrs. We intend to provide legal and political support."

Smith said the 10,000 members of CARD chose to hold local demonstrations rather than trying big national protests like those that took place during the height of the antidraft movment in the late 1960s, because they felt the fledgling antidraft-registration movement needed to do some "grass-roots organizing."

Benjamin H. Sasway, 21, who has publicly opposed the registration requirement at Humboldt State University in Northern California, where he is a political science major, last week became the first man accused of violating the mandatory draft-registration law enacted in 1980. A grand jury returned a one-count indictment against him in U.S. District Court in San Diego.