The D.C. City Council approved yesterday a $16.3 million, two-year budget supplement package that includes funds that are expected to be used for property tax belief in the city.

The package approved by the Council reduced by about $10 million a $26.4 million request submitted by Mayor Walter E. Washington, to whom the Council's budget plan now goes for approval.

Yesterday's action by the Council does not establish or propose an exact formula for reducing property taxes in the city. However, Council leaders, including Chairman Sterling Tucker, made it clear during six hours of the budget session yesterday that the additional money should be used to cut property taxes.

The council postponed until today a vote on a two-year supplemental capital improvements budget totaling $44.1 million. The capital budget package includes two potentially controversial items - $27 million to finance initial design and land acquisition costs for a proposed convention center in Mounty Vernon Square, and a request for $17 million to renovate Glenn Dale Hospital, the city's home for the chronically ill in nearby Maryland.

The two-year operating budget package is made up of a $10.8 million supplement to the city's fiscal 1977 budget and a $5.5 million proposed amendment in the fiscal 1978 budget, which is still pending before Congress.

The Council's $10 million reduction from the amount proposed by Mayor Washington involves several items that will mean cuts in some city services, including street lighting and street and alley cleaning. It also proposes that the Department of Human Resources receive $5 million less than previously allocated for welfare payments as a means of compelling DHR to purge its rolls of ineligible welfare recipients.

In recommending the cut in DHR's $100 million welfare fund, Tucker cited testimony Tuesday by DHR officials before a Senate subcommittee in which it was acknowledged that the agency is losing about $16 million each year due to an "excessively high" ineligibility rate.

The Council accepted the mayor's recommendation that a proposed reduction from twice to once weekly in trash collection for some areas of the city not be carried out. However, again at Tucker's urging and against strong protest from Council member Wilhelmina Rolark (D-eight), the Council cut $493,000 that had been earmarked for continuation of the current level of street and alley cleanings.

Rolark, who represents Anacostia, said she felt a reduction in alley cleaning would have a severe impact on low-income areas of the city because many of those areas already are slighted in the city's street-cleaning operations.

Earlier this year, the city's Department of Transportation had recommended removing nearly 9,000 street lamps in the city as a means of saving energy and doing away with some lighting that was considered excessive.

Yesterday the Council approved #631 000 to avoid turning off many of those lights, but said that an additional $631,000 requested to keep the lights on through fiscal 1978 could not be approved if the city is serious in its efforts to conserve energy.

Another area in which the Council approved considerably less than the mayor had requested was building security, where nearly $700,000 had been requested to beef up safety operations in city buildings following the March takeover of three buildings in the city, allegedly by 12 Hanafi Muslims.

The Council whose aides were among those persons held hostage, approved $201,500 to improve security during the remainder of the current fiscal year, but scaled down to $274,000 a request for an additional $490,000 in fiscal 1978. Until the mayor presents a comprehensive building security plan, the Council decided all the additional money should not be approved.

The Council also approved $250,000 to purchase the first phase of a $1 million vote-counting system that, when fully operational, will allow ballots to be counted in city elections in less than an hour.