Four members of a dissident Muslim group today charged they are being denied access to the Washington Islamic Center mosque because of racial or national discrimination and said they will seek relief from the District's Office of Human Rights.

Meanwhile, the center's board of governors, in an attempt to quell the dissidents' ongoing challenge to the board's authority at the center, is seeking a Superior Court injunction preventing 50 individuals who are alleged to be members of the dissident group from entering the center.

The board also is suing the dissident group for $170,000 for damages the dissidents allegedly caused at the center while it was under their control and for another $170,000 in punitive damages.

These actions are part of a three-year-old struggle for control of the Islamic Center. The dispute, an outgrowth of conflicting tendencies in the Moslem world, has prevented the normal functioning of the 35-year-old landmark on Massachusetts Avenue's Embassy Row.

The mosque's governing board is made up of the 29 ambassadors to Washington from Islamic countries that pay for the center's operations and upkeep. The ambassadors say they constitute the rightful authority in the center and can appoint its staff and religious leader.

But in 1980 a group including both foreigners and Americans challenged the board's authority, saying the ambassadors were Moslem "deviationists" who did not live according to the rules of the Koran. The group, whose leader is a 31-year-old American named Mohammad Asi, gradually took control of the center.

In March, special police hired by the board, armed with a U.S. Superior Court order recognizing the board as the legal owner of the mosque, forcibly ejected Asi from the center and regained control of the building. On July 15, dissidents returned to the mosque during services and were ejected by police. Since then, the center's special police have been screening worshipers at the gate to keep out the dissidents.

The four people who said they are filing a complaint with the Office of Human Rights are A. Hakim Qawiyy, an American; Aisha Mohammed, from Trinidad; Muhammad Siddiqui, from Grenada; and Massoumeh Roghani, from Iran. All denied ever trying to "interfere with a religious service at the mosque," the complaint said.

Their complaint alleges that the board of governors has "systematically and deliberately prohibited numerous Moslems from entering the mosque to participate in religious services."

Among those excluded have been "black persons from other countries in the world due to the fact that they are black; Iranians, due to their national origin . . . and Muslims who allegedly hold a specific or general political belief . . . contrary to the political view of the members of the Board of Governors . . . and persons who have been dressed casually or informally," the complaint states.

"Our sisters and brothers have today called upon the Office of Human Rights to halt this repressive conduct by the Board of Governors who have attempted to convert the mosque of the Muslims of this community into a country club for the privileged few," said Asi, whose group has complained that events at the mosque are a violation of religious freedom.

Their attorneys told reporters the complaint was filed yesterday, but a spokesman for the Office of Human Rights said he could not confirm receipt of an official complaint.

Qawiyy, one of the four complaintants, is listed among the 50 persons the board of governors has asked the court to prevent from going to the mosque. Asi and Bahram Nahidian, a vocal supporter of Iran's Islamic revolution, are also among the 50, who the board says "attempted to enter the mosque for the purpose of disrupting the religious services being held there" on July 15, and who the board contends will continue such disruptions if they are allowed to enter again.

The board's suit also alleges that the group "refuses to recognize the authority of the Board of Governors to manage the Center," including its authority to appoint a director and a religious leader for the mosque. The board also asked that the dissidents be ordered not to use the name "The Islamic Center" in its publications.