D.C. Mayor Marion Barry has abandoned his plan to slash the proposed fiscal 1982 budget for the city's public libraries by $2,779,000, deciding in the face of mounting criticism to restore more than half that amount in the money bill that is still in the drafting stage.

D.C. Public Libraries Director Hardy Franklin said Barry informed him in a letter on Tuesday that he would restore $1.5 million in proposed cutbacks. The library system still will face a reduction of $1,279,000 in its request for funds for operations during the year that begins Oct. 1. But the proposed -- and now rejected -- 26 percent budget reduction would have forced the closing of 6 of the city's 20 libraries and the layoff of 115 staff members. Barry's decision disclosed in the letter Tuesday removed that threat.

City Administrator Elijah B. Rogers, while not confirming that exactly $1.5 million would be restored to the library budget request, did concede that the mayor decided not to cut as sharply into the library proposal as he originally indicated would be done. Rogers said the initial reduction announced was only a preliminary figure, and always was subject to change once the administration had time to evaluate its impact. "No formal decisions have been made," Rogers said, "But we plan to give them some relief. The mayor felt that we could not reduce the libraries by that amount."

With $1.5 million more available in prospect, Franklin said, "all libraries presently operating will continue to opeate," no one on the library system's current staff of 400 will be laid off, and the library can begin filling at least some of the 20 staff positions left vacant by recent retirements.

Franklin said yesterday that $300,000 of the $1.5 million would be used by the library book fund to maintain the fund's current level of $710,000. The book fund is used to purchase books, records and other materials for the city's 20 permanent libraries, four community libraries (such as old storefronts converted for library use) and three "kiosks," which are small street outlets.

When the mayor began drafting his "austere" 1982 budget, to be presented for City Council consideration next month, among the most severe of the cutbacks was the proposed reduction in the library system's operating budget of $11,243,200. Franklin said the mayor then wanted to know what the system could do if he restored $250,000, $500,000 or $1 million.

The proposal to reduce the library request quickly became one of the most politically unpopular of the mayor's planned budget reductions.