The special commission created by Congress to oversee the District of Columbia's troubled financial management system reached a consensus yesterday to dissolve itself as soon as the city produces an acceptable plan for continuing to upgrade its procedures.

Sen. Thomas F. Eagleton (D-Mo.), who founded the Commission on Financial Oversight of the District of Columbia in 1976, told other commission members and city officials yesterday that the bulk of the special unit's work has been done and that he believed the city could complete the task on its own, with only routine supervision by the four standing congressional committees that normally oversee D.C. operations. f

Eagleton said the successful completion of the first full audit of the city's books, a separate report by auditors indicating that management of the city's finances had improved and a report from the commission's staff that pointed towards dissolution of the panel, all combined to "provide a clear direction for our future -- and that is to go out of business, or more precisely, discontinue active commission activities."

Commission aides said the unit technically could continue to exist for some time due to procedural delays. However, they said the consensus of the commission's closed-door session yesterday was that the panel would hold only one more meeting -- to approve a comprehensive plan for future financial management that the city is charged with submitting.

"The District has moved to the point where it can take charge of these activities," a smiling Mayor Marion Barry said after the meeting. "There was a general consensus that the commission ought to disengage."

Eagleton noted in an opening statement yesterday that the commission, working with funding of $38 million, had two primary tasks: To design and put in place a modern accounting system, and to complete a full-scale audit.

He noted that in October 1979 the city began operating its new computerized accounting system, which was designed largely by members of the commission staff. Earlier this month, independent auditors completed the first full-scale review of the city's books in history.

With the help of the commission, the District is making the conversion to a form of accounting and financial management suitable for a city," said Eagleton, who noted that a prime reason for establishing the special unit in the first place was that "the District books were found to be in such disarray as to be unauditable."

Staff members said the commission still holds $9 million in unspent funds. The report that the city must submit before the commission ceases its activities must spell out ways to spend that money to further improve financial management, as well as ways to alleviate accounting problems that persist even after five years of oversight by the special panel.

"We are all familiar with the problems -- computer malfunctions, lack of key financial personnel in the District, necessary design changes, documentation, insufficient training," Eagleton said.

Barry estimated that it would take from one to two months for the city to complete its final plan.