D.C. Corporation Counsel Inez Smith Reid said yesterday that her office has nearly exhausted the $5 million set aside this fiscal year to cover settlements and judgments stemming from lawsuits against the city and she asked that the City Council approve an additional $1 million.

"The whole problem of lawsuits against the city is burgeoning," Reid told members of the council's Judiciary Committee. "Cities nationwide are experiencing a veritable explosion in municipal liability."

The request was made a day after a D.C. Superior Court jury ordered the District to pay $250,000 in damages to a 15-year-old girl who five years ago was lured out of an unsupervised classroom in a Southeast Washington school and sexually assaulted.

In documents filed in court, lawyers for the city denied any negligence. Reid described the case as "highly sensitive" and said the judgment has placed added budgetary pressure on her office.

Reid defended her office's peformance in trying to minimize the District government's financial vulnerability in litigation, which includes personal injury, property damage and false arrest claims, and claims of civil rights violations and discrimination in employment.

However, she said that the "gradual erosion" of special defenses available to governments and the sharp increase in the number of suits brought under a federal civil rights statute have opened the floodgates to litigation.

Some municipal law specialists have estimated that the cost of settling damage claims against cities has tripled during the last five years.

Civil rights cases can be especially costly to the District and other cities, Reid said, because plaintiffs who win are entitled to recover the cost of their attorneys' fees, which often far exceed damages.

"This office will continue to devote its resources to minimizing recoveries against the District, and will continue to seek reversals of unjustifiably inflated jury awards," she said. "However, the general tendency to higher verdicts is a fact of life which must be dealt with."

As of May 10, the Corporation Counsel's office had spent $2 million of the $2.8 million budgeted for out-of-court settlements and had spent $2.1 million of the $2.2 million set aside for judgments.

Reid has asked the City Council to approve $1 million in supplemental funds for the current fiscal year, which ends Sept. 30.

Reid has also sought approval to spend $41,000 of city funds to hire additional staff to handle a $400 million lawsuit brought by D.C. government agencies and the Board of Education against 40 companies that manufacture and distribute asbestos that was placed in city buildings.

"This lawsuit has national significance since it is one of several efforts . . . to obtain compensation for hazardous and life-threatening conditions resulting from exposure . . . to dangerous asbestos fibers," she said.

James Palmer, director of the D.C. Department of Corrections, also appeared before the Judiciary Committee, seeking support for a $4.5 million increase in his agency's fiscal 1985 budget, including funds to handle a burgeoning prison population.

The department originally assumed, in seeking funds for the current year, that it would handle an average of 5,784 prisoners per day in D.C. corrections facilities, according to Palmer. But officials now say that the prison population will average 6,300 by the end of the year -- 500 more than originally projected -- and officials are seeking an additional $1.15 million to house prisoners.

Palmer also asked for nearly $3.4 million for a bonus for department employes, repairs at Youth Center 1 at Lorton and inmate drug programs.