A major New York investment banking firm has recommended that Mayor Marion Barry create a top-level committee of officials to oversee District of Columbia finances and prevent a recurrence of the cash squeeze that threatens a cutback of city services.

The proposal was made by staff members of Lazard Freres & Co., which has served as a financial adviser to the District under a contract signed last summer -- months before the current crisis emerged. for the moment, the city is paying no fee to Lazard Freres.

Barry said of the proposal last night, "We're discussing it," and added that he and his financial staff will meet on the recommendation today.

Asked if he was disposed toward accepting the proposal, Barry replied, "Of course I am." He said that his top financial advisers already have formed such a panel informally to deal with the city's current budget crisis.

Lazard staff member Eugene Keilin said the panel "is designed to . . . anticipate . . . and prevent (the) type of problem" now confronted by the District. Officials are moving to cope with a budget deficit officially estimated as high as $84.5 million.

"The city has some short-term problems but it is not on the brink of default or bankruptcy," Keilin said.

Budget Director Gladys Mack said yesterday that the $84.5 million figure is being used as the highest net cash shortage that the city is likely to face between now and the end of the fiscal year on September 30. A $92 million figure was attributed to Barry after a news conference last Friday, but Mack said that was based on a misreading of a tabulation.

City Council members and Barry, meanwhile, sparred yesterday over the true size of the gap between projected revenues and expenditures. Betty Anne Kane (D-At-Large) circulated a memo saying the figure could rise as high as $175 million and calling for a package solution of cutbacks and tax increases rather than a piece-meal approach. Shown the memo, Barry told reporters, "I think she's grandstanding."

The exchange came on the eve of a second meeting today between Barry and the full Council membership on the financial situation. Barry said he will not be ready to tell the Council yet what cuts in services and payrolls he will seek to impose.

Collin S. Walters, the city's assistant administrator for financial management who resigned under pressure effective March 21, met with two Lazard Freres staff representatives yesterday.

All three, questioned by reporters, said Lazard's relationship with the District began months before the current crisis and was not spurred by it. They said it is part of an overdue shift of the District from its traditional federal government accounting system to one tailored for a city.

Keilin, one of the Lazard staff members assigned to work with District officials, is an expert in big city financial distress. He was executive director of New York's Municipal Assistance Corp. (MAC), a state body set up in 1975 to oversee the bail-out and retrenchment of New York City finances, Felix Rohatyn, a top Lazard official, served as MAC chairman.

Walters said the District solicited proposals from several firms soon after Barry took office in January, 1979, leading to the choice of Lazard to act as the city's long-term financial adviser. He said the advice deals far beyond immediate cash-flow problems.

One key purpose is to permit the city to sell bonds on the open market, rather than borrowing from the U.S. Treasury, to finance construction projects.

Walters said the District's first bond offering probably will not come earlier than 1981. Lazard will receive a fee based on the size of each bond sale, and is not receiving any city funds meanwhile.

"The city must balance its budget and keep it balanced, or it will never borrow," Keilin said.

In a related development, the Mayor sent the Council a reorganization plan that, if not blocked by Council resolution, will shift the D.C. treasurer's Office out of the Finance and Revenue Department and into the office of financial management now held by Walters.