The Fairfax County Redevelopment and Housing Authority, escalating its dispute with Northern Virginia Republican Rep. Stanford E. Parris and the Reagan administration, has retained the prestigious Washington law firm of Covington & Burling to prepare a lawsuit against housing secretary Samuel R. Pierce Jr.

The suit would be aimed at securing more than $2 million in federal funds for a proposed public housing project in western Fairfax. Federal housing officials approved the $2.4 million project more than a year ago, but opposition from Parris and neighboring homeowners caused federal housing officials to delay it several times.

The 44-townhouse project on O'Day Drive west of Centreville is the fourth in the metropolitan area that Pierce's office has delayed or derailed during the past year. A Springfield project for which the Fairfax authority already had chosen a contractor was killed when local civic associations persuaded Parris to use his influence with top housing officials.

A lawyer from Covington & Burling threatened legal action in a June 30 letter to Pierce, calling the delays illegal and possibly discriminatory, and asked for a response by last Wednesday. Gerald W. Hopkins, chairman of the Fairfax authority, said yesterday that Pierce has not responded and that the authority will meet Tuesday night to authorize the lawsuit if nothing has changed by then.

"We have an administration that is pushing community control and pushing community choice, and it's very interesting that the congressman's office and the Department of Housing and Urban Development central office would be delaying a project that the local jurisdiction has said it wants," Hopkins said.

Parris, who is running for reelection from a district that includes Alexandria and half of Fairfax, has said he opposes public housing if it is too expensive or if residents near the proposed sites do not want it. The congressman, a member of a House committee that oversees federal housing programs, could not be reached for comment yesterday. His ally in opposing the project, Fairfax Board Chairman John F. Herrity, yesterday criticized the authority for "wasting money" on expensive Washington lawyers.

Fairfax County, with more than 600,000 residents, has only about 500 public housing units and proposals to build projects almost always generate controversy. County officials planning the O'Day Drive project encountered strong opposition for more than two years and responded by reducing both the size and cost of the project before letting a contract for a new access road, which is now about half built.

The authority now proposes to spend approximately $2.4 million, or $55,000 per house -- down from the $3.1 million cost that was projected before Parris intervened in January. Last month, however, HUD officials put another hold on the project without explanation, Hopkins said.

A spokesman for Pierce yesterday said he could not comment until he had studied the documents involved. Pierce's assistant, Philip Abrams, said during a previous delay in February that the administration believes the government should renovate its dilapidated projects before building new ones, but that in the case of O'Day Drive the secretary only wanted to ensure that proper cost guidelines were followed.

Fairfax Board Chairman John F. Herrity said housing officials had told Parris and others in a meeting last month that they could not stop the O'Day project because HUD already has signed a contract. Herrity criticized the authority for "hiring high-priced legal talent, high-priced consultants and wasting money building $100,000 units."

Authority director Walter Webdale said that the one county attorney assigned to his department cannot handle the legal workload by herself.