The D.C. City Council, beginning its third year of government under home rule, took the first formal steps yesterday to strip away the prestige and power of Councilman Douglas E. Moore (D-at large).

Only hours after newly-elected and re-elected members were sworn in on the steps of the District Building, Council Chairman Sterling Tucker introduced a reorganization plan that would remove Moore as chairman of the Council's powerful budget committee.

The Council scheduled a vote on the plan for next week, at which easy-passage is expected. The Council then voted to replace Moore as chairman pro tempore of the council, a largely honorary position but one whose power is expected to be increased under the reorganization plan.

The two actions jointly will leave Moore as the only one of the council's 13 members who will not head a committee or hold any other council post. It would also decrease any likelihood that the controversial minister could come to head the council in the event that Tucker vacates the chairmanship either to run for mayor or replace a resigned Mayor Walter E. Washington.

There has been considerable speculation in District political circles that Mayor Washington may not complete his remaining two years in office. This speculation has him either accepting an appointive position in the federal government, or even being forced out of office by continuing allegations of mismanagement in city government.

Moore refused yesterday to be discouraged by the loss of power. "It has enhanced me in the eyes of my constituents as unbought and unbossed," he said after the meeting. "I will continue to do my work whether I am a committee chairman or not."

Moore blamed his loss of power on his opposition to an "agenda" set for city government by the Metropolitan Washington Board of Trade, and a deal between Tucker and Councilman Marion Barry (D.-at large) over the 1978 race for mayor and City Council chairman.

"They have very skillfully put together an agenda for '78 and have set the stage for who will run for mayor and chairman of the council," Moore said. "The Board of Trade feels that if by '78 they could totally eliminate Rev. Douglas Moore, then they would have no opposition."

Moore will be replaced as chairman pro tempore by Council member Willie J. Hardy (D.-ward seven), who was elected after being nominated by Barry. Tucker will replace Moore as chairman of the budget committee, whose membership will be expanded to include all 13 members of the council.

Moore's loss of power had been anticipated for weeks, as many council members complained privately that they felt that he had not done an effective job as budget committee chairman, and had frequently been absent. They also expressed concern about well-publicized personal incidents involving Moore that became controversial.

In June, Moore was convicted of hitting and biting a 19-year-old tow truck driver behind the District Building. Three months before that, he was found guilty of unauthorized use of dealer's tags on his personal car.

Moore said yesterday that the allegations that had not worked hard as budget chairman and had frequently been absent were inaccurate.

Similar accusations, he said, could be made against those who were accusing him.

Tucker first proposed the reorganization plan on Dec. 13, at an unannounced day-long meeting at the International Inn.

In addition to abolishing Moore's committee chairmanship, the new plan would merge the public safety committee, formerly headed by Mrs. Hardy, with the judiciary committee, headed by David Clarke (D-one). Clarke would be chairman of the new committee.

The plan also would merge the higher education committee, formerly chaired by William Spaulding (D-five) with the education, recreation and youth affairs committee, headed by Julius Hobson (Statehood-at Large), Hobson would be the new committee chairman, while Spaulding would be made chairman of the administration and personal committee.

Tucker plans to increase the prestige of the chairman pro tempore position by giving Mrs. Hardy other responsibilities outside the council. Among these, Mrs. Hardy said yesterday, she anticipates replacing Tucker as one of the council's representatives on the Metro Board in the spring.

In his lone opposition yesterday to the nomination of Mrs. Hardy, Moore argued that it would be futile to select a chairman pro tempore who is not an at-large member of the council because the city charter provides that only an at-large member may be elected acting chairman in the event that the chairmanship is vacated in mid-term.

Moore tried to place in nomination all three of the other at-large members - Hobston, Barry and Republican Jerry A. Moore - but all three declined.

District political observers believe that the reorganization could bring to the fore two years of internal jousting between Barry and Tucker, both of whom are considered likely candidates for mayor in 1978.

One new council member was sworn yesterday, and five others re-elected to second terms in the November general election also were administered oaths of office.

The new council member is Democrat Wilhelmina J. Rolark, a lawyer and the wife of newspaper publisher Calvin Rolark, who defeated incumbent and fellow Democrat James Coates for the right to represent ward eight in far southeast Washington.

Sworn in for second terms were at-large members Barry and Jerry Moore, along with John A. Wilson (D-two), Arrington Dixon (D-four) and Mrs. Hardy.

Under the 1974 home rule charter, which gave the city its first elected government in 104 years, the seats of the other seven council members, as well as the mayor's office will be up for election in 1978.