The son and spiritual heir of the founder of the influential Black Muslim movement in America has disbanded the separatist organization, urging his followers to remain faithful Muslims but within the worldwide Islamic community.

"If you follow my advice, you would put down the term 'American Muslim Mission,' " the name by which the mainline black Muslim group has been known in recent years, Warith Deen Muhammad told his followers recently. "You would put it down and never pick up any term that lumps you all together in one community. You would be members of a Muslim community that's international."

Muhammad announced the dissolution of the organization that his father, Elijah Muhammad, helped found more than a half century ago, in simultaneous telephone hook-ups from Chicago to five centers across the country, including Washington.

Munir Um'Rani, acting editor of the organization's newspaper, the weekly American Muslim Journal, said yesterday in a telephone interview from Chicago that response to the April announcement has been "very positive. It's a sign of religious freedom. We're not confined by terms such as 'American Muslim Mission.' "

Imam Adil al Aseer of the Islamic Center here praised the action as a move in harmony with fundamental Muslim principles. "We are against discrimination," he said, adding that Warith Muhammad has "brought the real Islamic ideas" to his people.

Warith Muhammad was designated at birth to succeed his father as head of the organization of Black Muslims, and took over when his father died 10 years ago. But he has consistently nudged his followers closer to the mainstream of both American life and conventional Islamic principles, and away from the separatist community that Elijah Muhammad built up as a bulwark against what he saw as a racist and exploitative white-dominated society.

Warith Muhammad discouraged references to "white devils," and whites as well as blacks were welcomed to worship services and to membership in local mosques. He encouraged black Muslims, for the first time, to register to vote in the 1976 elections.

The founder's son changed the official name of the group, first to the World Community of Islam in the West, then to the American Muslim Mission. He changed his own "un-Islamic" first name of Wallace -- after Wallace Fard who initiated the movement in Detroit in 1930 -- to Warith.

Local imams, as Islamic leaders are called, were encouraged to develop ties with other Muslim leaders as well as with leaders of other faiths. Muhammad himself participated in a historic exchange of visits with Rabbi Joshua Haberman of the Washington Hebrew Congregation here.

While many in the movement accepted the changes, which covered many of the reforms Black Muslim Malcolm X had fought for, others resisted and broke away in sometimes bloody schisms.

A segment led by Louis Farrakhan has retained both the name "Nation of Islam" and racial separatism, as well as the paramilitary trappings of the elder Muhammad.

Um'Rani said membership figures for the American Muslim Mission are not available, but there are approximately 200 masjid, or local mosques, around the country.

Imam Sultan Muhammad, who heads the local American Muslim Mission activities, was out of town and could not be reached for comment on what effects the change may bring in the Washington area.

Um'Rani said negotiations are under way to sell a number of properties owned by the national body, including a farm in Georgia and a site being developed for a college in North Carolina.

Elijah Muhammad, who died without a will, fathered 21 children, some of whom are still locked in a legal battle with the mission for control of portions of his property.