Housing and Urban Development Secretary Samuel R. Pierce this week gave a provisional go-ahead to a controversial public housing project in the Virginia suburbs that he delayed last month at the request of Republican Rep. Stanford E. Parris.

Pierce said Fairfax County may build the 44-town house project in Centreville if its projected cost is reduced by about one-tenth, from $2.63 million to $2.39 million in federal funds.

The secretary had encountered increasing criticism for responding to pressure from Parris and from neighborhood opponents in Centreville and three other proposed project sites in the Washington area. A national advocacy organization accused Pierce in a letter last week of unwittingly promoting racial discrimination in Fairfax County. The U.S. Commission on Civil Rights last month began investigating federal housing policies there as a result of the public dispute.

Top aides to Pierce rejected the criticism yesterday and said it had no effect on the secretary's decision on the Centreville project. "We spend 80 percent of our time trying to move projects forward and only 20 percent of our time investigating questions that involve stopping projects," said Philip Abrams, general deputy assistant secretary for housing. "Congressmen, citizens, Republicans, Democrats--we're open to anyone who wants to talk to us."

The Centreville project is at least the fourth that Pierce's office has delayed or derailed in the metropolitan area during the past year. The HUD central office intervened twice in Montgomery and in one other case in Fairfax, essentially killing those three projects, officials said.

Both Gerald W. Hopkins, chairman of the Fairfax housing authority, and Bernard L. Tetreault, executive director of the Montgomery authority, said the central office had never before intervened to block a project in their 10 years' experience.

"We've had citizen opposition, but as long as we followed the processes you could expect that HUD would sign when they had to sign," Tetreault said. "We're very disappointed this whole past year with the substantial opposition we've had and the change in the environment generally."

The administration's proposed budget for fiscal year 1983 contains virtually no funds for new construction. Abrams said yesterday that the government should renovate its dilapidated public housing before building new homes.

Abrams said, however, that Pierce had not been acting on that policy when he delayed the Centreville project last month or the other three projects in Springfield, Germantown and Colesville. Abrams said the secretary only wanted to make sure proper procedures and cost guidelines were followed. In each case, Abrams said, Pierce ruled the proposals were too expensive.

Neighbors had opposed the Centreville project, slated for a 14.6-acre site at the corner of O'Day Drive and Lee Highway in Fairfax's westernmost corner, since county officials announced their plans in 1980. Parris, who sits on the House committee that oversees federal housing programs, began protesting last spring. On Jan. 11 Pierce informed the congressman that he had frozen all funds for the project pending an investigation.

The National Committee Against Discrimination in Housing objected to Pierce's action in a letter dated Feb. 5. The organization, which has brought open housing lawsuits since the 1960s, charged that the delay threatened the construction of the Centreville project.

"Your action could have a disproportionately greater adverse impact on blacks than on whites, exclude blacks from a predominantly white area, and perpetuate existing patterns of racial segregation in housing," committee director Martin E. Sloane wrote.

Fairfax County's population of 600,000 is about 6 percent black and close to 15 percent minority, including Asian and Hispanic Americans. Tenants of the county's 500 public housing units are about 60 percent white and 40 percent minority, said a spokesman for the Fairfax housing authority.

A spokesman for Rep. Parris denied that race was a factor in the opposition to the Centreville or the Coventry project, which Parris opposed last year. "The question of black and white has never been mentioned on O'Day or Coventry in any of more than a hundred meetings we've sat in on," the spokesman said.

Parris said he opposed both projects because of their cost and because of neighborhood opposition. His spokesman said yesterday he is not convinced the authority will be able to bring its project within the cost limit demanded by Pierce.