Benjamin H. Alexander, president of the University of the District of Columbia, said yesterday he plans to resign next month because he believes he can no longer accomplish the goals he set for the university under continuing opposition from some trustees and faculty members.

"I just felt I could not accomplish the job I wanted to do with the restrictions that were there," Alexander said in an interview.

Ronald H. Brown, chairman of UDC's Board of Trustees, said that he had planned to issue a joint statement on the matter with Alexander on Monday. "I regret he chose to move forward with a statement on his own," Brown said. "However, the board and I wish him well."

Brown declined to comment on Alexander's reasons for leaving.

Marjorie H. Parker, a trustee and board chairman when Alexander was appointed, said last night that she had no comment on Alexander's announcement. However, in recent months Parker has expressed growing concern over Alexander's leadership style and his suspension of more than a thousand students for poor academic performance.

Another trustee, Terry B. Thomas, said, "I supported Alexander all the way. I guess he just thought his hands were tied." Thomas was one of four trustees on the 15-member board whose support for Alexander remained constant.

Alexander's announcement capped weeks of rumors that UDC's board was considering firing him. Alexander, who became president almost one year ago, said he was well aware of the rumors, but that "no one ever asked me to resign, no board member threatened to fire me."

He said, however, that his supporters "were ready to go to war" to keep him, but added that "all they would have gained was a big fight in the press and the school would have been the loser."

Alexander, a former D.C. school board member and president of Chicago State University before his UDC appointment, said he believes the community and the students were always more supportive of him and his policies than the faculty and the board. He said that while his initial reaction to the rumors was to "stay and fight this thing," he realized in the last week that the situation was growing "worse, worse, worse." He said he did not want to provoke a battle that pitted blacks against blacks, which he believed the debate over his proposals and administrative style was doing.

"I love this university too much to see this kind of thing happen. The university deserves more, the city deserves more," said Alexander, who took over as president last Aug. 1. "I'm not bitter, I'm not angry. I look at this as, this job's not for me."

He said that his greatest problems were the restrictions placed on him by the trustees. He said he was prohibited from starting new programs, and from hiring teachers or transferring employes within the university. Those board actions, he said, "stripped my staff and me of all power of running the university. . . . If I wanted to transfer a person from one department to another I couldn't do it without board approval."

The UDC board of trustees was split 7 to 6 in favor of Alexander's appointment when it voted to hire him in March 1982. Over the last year, the board members who initially opposed Alexander continued to have sharp criticisms of his administration.

In the last year, Alexander lost the support of two board members who had voted for his appointment: Parker and Alton Wilson, who died shortly after Alexander was appointed.

Alexander said yesterday he was told before he accepted the job that he would have the support of the vast majority of the board and that he would not have taken the job if he had known the division among the board members was so severe.

The Alexander appointment created controversy even before it became official. The faculty leadership tried to block his appointment and then when he did get the job, they, some trustees and students tried to get the court to overturn the appointment, arguing that it was made under faulty procedures.

Alexander said yesterday his faculty opponents have remained critical of him throughout his tenure and that, with his original support on the board eroding, he felt "the best thing to do would be to resign."

Alexander said yesterday he believes his leadership style displeased some trustees. "People have told me it's your style--you're impetuous, you're trying to do too much. My feeling has always been if something needs to be changed you ought to do it as quickly as possible."

The trustees rebuffed Alexander on the one major change he proposed: a reorganization of the university's administration that would have included dismantling the "university college," the program that deals with the school's remedial reading and math and tutoring programs. Alexander said the school should continue the services for some students, but maintained that such a heavy concentration of programs was no longer necessary because the14,000-student university was gradually getting better prepared students, and the program was a "stigma" on the school.

But a majority of the board rejected his view, maintaining that the open admission school has a special responsiblity to helping those students ill-prepared for college work.

Alexander had signed a three-year contract with the board that gave the board the right to fire him with or without cause. A source close to the board said yesterday that it had agreed to pay Alexander his $59,500-a-year salary for the rest of the contract, or until Alexander finds another job.

Alexander said he would like to work for the federal government "helping the poor and disadvantaged get an education."