Two different Islamic religious groups demonstrated in Washington yesterday in an afternoon of peaceful protests.

About 100 members of Washington's international Islamic community demanded that the Islamic Center at 2551 Massachusetts Ave. NW be reopened after the center's board of directors closed the mosque last weekend and ousted a religious leader who had been living there.

The other group, about 300 Washington members of the American Muslim Mission, picketed the Federal Bureau of Investigation headquarters at Ninth Street and Pennsylvania Avenue NW, claiming that a year-old court decision was part of an FBI plan to tie up assets of the national American Muslim Mission.

Moslems at the Islamic Center protested last week's closing as a violation of their right to religious freedom.

They gathered outside the mosque and held their Friday prayer service on the sidewalk after police prevented them from going inside the building. There were no injuries or arrests reported.

The worshippers were followers of the Imam Mohammad Asi, the fundamentalist religious leader evicted last week from the center by a private security force hired by the center's board of governors, which is made up of ambassadors from Islamic countries represented in Washington.

Yesterday's events were a continuation of a long-running controversy between the center's governing board and a group of Moslems led by Asi who dispute the board's authority to appoint the Imam or spiritual leader of the mosque.

Asi claims he is the Imam because he was elected by his followers.

Asi said he and his group would be willing to discuss the conflict with the Board of Governors if the board is willing to resolve the issue "according to the principles of the Koran" but not "if they want concessions or negotiations from a power position."

In a news release last Tuesday the Board of Governors said that "until the demonstrations cease, the mosque and the center will remain closed for public safety."

Meanwhile, later yesterday afternoon, Muslims who belong to the American Muslim Mission protested what they said was FBI involvement in their internal affairs.

The demonstration in front of FBI headquarters was planned to coincide with a larger march of about 1,000 Muslim demonstrators in Chicago that included Muhammad Ali, according to the Chicago Tribune.

The demonstrations were based on the results of a February 1982 court case in which the heirs of the late Elijah Muhammad, head of the mission once known as the Nation of Islam in the West, won rights to $4.6 million in assets that the mission has claimed is the property of its members.

"We are not going to allow our property to be taken away," said Sultan Muhammed, Imam of the Washington Masjid of the American Muslim Mission, who led the hour-long local march yesterday.

"Elijah Muhammad stood for building a nation of Muslims, not for making his heirs rich. His heir should know that this money should stay in the community."

A mission news release yesterday contended that the court decision, handed down by Cook County (Ill.) Circuit Court Judge Henry Budzinski, "is part of the continuing 'Hoover' plan revealed in COINTELPRO documents," referring to the FBI counterintelligence program designed to splinter New Left groups in the 60s and early 70s.

FBI spokesman Ed Gooderman said the FBI had no comment.