District Mayor Marion Barry has asked the City Council for $5.2 million to complete construction of the municipal center at 14th and U streets NW, but some council members, disturbed by delays and construction problems at the site, are challenging the request.

Council member Nadine P. Winter (D-Ward 6), chairman of the council's Public Works Committee, has filed a formal notice of disapproval of the mayor's request, which calls for a transfer of funds originally earmarked for improvements at the aged District Building to the new Frank D. Reeves Center.

Winter's aide, David Watson, said Winter intends to question city Department of Public Works officials closely at a hearing next week on why the extra money is needed.

Public works officials said in an interview two weeks ago that while construction of the municipal center was 12 months behind schedule, the delays would not substantially add to the costs.

John Touchstone, District director of public works, said the city government was "lucky" to have completed construction of the basic structure within a 1978 budget of $35 million.

But in a letter to City Council Chairman David A. Clarke, Barry said the Public Works Department needs an extra $1.5 million "due to unanticipated schedule delays and design modifications," in addition to $3.7 million to finish interior work on the building.

Council member Betty Ann Kane (D-At Large) said she would vehemently oppose funding completion of the municipal center with money designated for repairs at the District Building, which she termed "a firetrap."

She said the problems at the municipal center reflect a lack of "any sort of proper supervision" of the city's construction contracts and that they are "typical of the shoddy construction that the city is engaged in."

John A. Wilson (D-Ward 2) agreed, commenting, "This is across the board. The whole contracting process needs to be looked at -- who we're doing it with, how we're doing it and why we get all the substandard people all the time."

Barry blamed the delays on a church official who refused to sell a piece of property in the middle of the site, a window contractor who was "significantly delinquent in delivering the building's custom-made glass windows and exterior doors," and design modifications.

He said the choice of a fast track method of construction, in which design and construction proceed simultaneously, compounded the problems.

While the fast track method has "many advantages," Barry said, "project coordination is simply more difficult" and delays can be particularly costly.

The mayor added that the costs attributable to the delays are "equal to 3 percent of the project budget and are well within the acceptable range for industry standards."

Barry said the balance of the request -- $3.7 million for interior work -- was not included in the original budget because city officials at the time did not know which District employes would be occupying the building or what their office needs would be.

The mayor said he did not expect to ask for additional funds, but he warned that "as with any major construction project . . . claim settlements may be needed upon close-out."

The claims by contractors related to delays may amount to as much as $1 million. Executives of the Sherman R. Smoot Corp. of Washington said they plan to file for $600,000 to $700,000 in added costs, largely attributable to delays; another contractor has filed for $165,000, and the city has awarded a third contractor $36,000 for delays.

In a brief interview yesterday, Barry defended the project, saying, "You check out anything that is a $40 million project, see what problems you have."

He said that because of the build- ing, the Shaw neighborhood, which has been ravaged by crime and riots, "will be revitalized."

The full council has until March 7 to act on Winter's challenge to the mayor's request for an increase.

If no action is taken, the increase is automatically awarded.

Wilson, who chairs the council's Finance and Revenue Committee, said that while he intends to scrutinize the mayor's request closely, "They'll get it."

"You can't stop it in the middle of the building, and the other problem is, it's the mayor's showcase of economic development in that area."

He said the problems at the municipal center, which have ranged from cracked concrete beams to doors that would not close, illustrate that "we were not even monitoring what we were getting and what we're paying for."

"Look, it's a disaster," Wilson said of the contracting process. "It doesn't make any difference if it's minority contractors or . . . majority contractors, it seems like it's always a problem."

Contract files and interviews with numerous contractors show that contractors who did not perform as expected and District project managers who did not stay on top of the job have contributed to the slow progress.

A potentially serious problem involving structural support for four elevated walkways has not been fully resolved.

District officials are waiting for a report from the city's construction management firm on whether repairs made in December 1984 have fully corrected the problem of cracks in concrete beams that help hold up the walkways.

Watson, Winter's aide, said the council member wants to question District public works officials "about the lingering concerns about the structural integrity of the building," as well as about the added costs.

"She would like a little more than a broad explanation," added Watson.