Snow and ice removal during last month's unusually heavy storms cost the District of Columbia government more than $2.1 million -- seven times the amount that had been appropriated in the city's budget.

Mayor Marion Barry yesterday asked the city council for $1.8 million to pay for salt and sand, overtime wages, plowing by private truckowners and the mammoth job of patching the numerous potholes caused by the storm.

In submitting a $76.8 million supplementary budget package to the council -- the second such spending request from the mayor in less than a week -- Barry and other city officials said that even more funds may be required once the full cost of the storm is known.

Only $303,000 was in the District budget for snow and ice removal. Most of that money was for the estimated costs of handling "a couple inches of snow and that would be all," said Bernard J. O'Donnel, deputy director of the D.C. Department of Transportation. It included, for example, about $35,000 to pay the owners of 130 private trucks a seasonal fee of $275 just to attach snowplows to their vehicles in the event that such trucks would have to be used to help the city plow the snow.

"But that fee is just to carry the plow around if we never call on them," O'Donnell said. The city did have to call on these drivers last month and their charges eventually totaled $306,800.

Barry also asked yesterday for $416,500 to pay for more than 35 tons of salt and sand that were used, $669,000 in overtime pay for city workers and $334,000 for vehicle parts, supplies and other minor equipment.

The moyor also asked $73,700 for pothole repair but O'Donnell said that was only a "token amount." Much more eventually will be required.

In one five-day period alone last week, the city spent about $325,000 patching potholes -- the amount that is budgeted for that purpose for the entire year, O'Donnell said. One-third of those repairs were temporary, he said.

City budget director Gladys W. Mack said none of the money in the supplementary budget is for the purchase of new snow-removal equipment. "An inventory will be taken on the need for additional equipment. If we determine we need equipment it would have to be considered" in still another spending request, she said.

O'Donnell said that new equipment probably will not be purchased because even though such equipment would hasten plowing operations in drastic situations such as those of last month, such heavy snow is rare in Washington.

"You could build more in and buy all that fancy equipment, but it just rusts," he said. "It would allow you to do somebody's street 10 hours faster, but is it really cost-effective?"

The $1.8 million for snow removal and pothole repair was the mojor part of a second supplement submitted by Barry to the budget for the current fiscal year. Combined with a request for $60,600 for publication of the District of Columbia code and a $79.8 million request made by the moyor last week, yesterday's submission brings to $81.6 million the amount in additional operating funds that the new mayor has requested for the current fiscal year which ends Sept. 30.

Barry also asked yesterday for an additional $44.9 million to operate the city during the 1980 fiscal year and $30.1 million for public works projects in fiscal 1980.

Most of the public works money, $26.7 million, would finance the purchase of Metrobus equipment and Metrorail construction costs. Another $3.4 million would pay the costs of installing smoke detectors in city facilities -- including housing projects, hospitals, health care and penal institutions -- as required by a law enacted last year by the City Council.

Barry proposed yesterday to continue in 1980 a youth jobs program that is expected to begin this year. He asked the council for $13.7 million to provide 12,614 jobs for youths -- most of which would be nine-weed summer jobs for persons 14 to 21 years of age. Funds are also included for part-time jobs for high school students and some full-time positions for persons out of school.

Barry also proposed spending $1.3 million to increase the level of government subsidies given to private agencies that provide day-care facilities for children from low-and moderate-income families. Budget officials could not say yesterday whether the increased spending will mean that more children could be enrolled in day care programs. But by increasing from $10 to $12 per day the subsidy allowed, the Barry administration hopes to encourage more day-care providers to serve lower-income parents.

The budget proposal submitted yesterday also includes $3.5 million to develop community care facilities for patients now at St. Elizabeths hospital and $1.5 million to help comply with a court order that the city improve care at Forest Haven, the District's institution for the mentally retarded.

Barry asked for money to increase the size of the staff in the corporation counsel's office, the office of the city administrator and his own office. He also proposed to finance with city funds the D.C. office of business and economic development, which now is funded by federal grant money. In that office, Barry proposed implementing a $30,000 project to provide a one-stop business registration center and a $150,000 program to launch a neighborhood revitalization program.

Barry said yesterday that no tax increases would be required to finance his addition to the already proposed $1.4 billion operating budget pending before Congress.