Mayor Walter E. Washington asked the District of Columbia City Council yesterday to approve a $70.4 million, two-year "inflation relief" and capital improvements package.

Included in the proposal are funds to plan a downtown convention center, temporarily reduce the city's property tax rate and increase security at city government buildings.

The proposed spending increase also would provide money to finance the city's share of operating deficits for the Metrorail sytem.The mayor had been holding back requests for funds in an effort to prod other area governments into developing a regional susidy plan.

Funds also are requested to avoid a proposed reduction of trash collection in some areas of the city from twice to once weekly and to continue street lighting in some neighborhoods where reduction sahd been urged to save money.

The mayor said the proposal "makes sense for our city and is economically sound." The proposals "have been tailored to meet the need to maintain vital public service levels in these difficult times while providing a measure of tax relief to our residents," he said.

If the mayor and the City Council agree on the package, which includes a $29.7 million supplement to the city's 1977 budget and a $40.7 million amendment to the proposed 1978 budget, Congress must approve the spending. The current budgets for fiscal years 1977 and 1978 are about $1 billion each.

The proposed property tax rate reduction would lower the present rate of $1.83 per $100 of assessed evaluation by 4 per cent to $1.76. That would amount to a $35 reduction for the owner of a $50,000 home.

The mayor's tax relief proposal would apply only to the current tax bill that is due Sept. 15. Next year, the city is assuming a return to the $1.83 rate. The one-time reduction would be an across-the-board cut for both residential and commerical tax-payers.

At a press conference immediately before the mayor's announcement, Council member Marion Barry (D-at large), chairman of the Council's finance and revenue committee, proposed a tax relief plan that Barry said would be geared to give special benefits to homeowners.

Barry's plan would allow all owners of four or fewer singles-family units to deduct $6,000 from their property tax assessments before the $1.83 rate would apply. Barry said his plan would amount to a tax savings of almost $110 for every homeowner in the city.

"Citizens are irate and disheartened about their assessment increases, and I don't blame them for feeling that way," Barry said. "The homeowner's exemption bill . . . goes to the heart of the problem by actually lowering everyone's assessed value by $6,000."

Barry's plan was cosponsored by the entire five-member finance and revenue committee and immediately won the backing of Council Chairman Sterling Tucker, who chairs the Council's budget committee.

Tucker said, he will propose two amendment to Barry's bill that would increase the amount of "circuit breaker" tax relief available to low income residents and set a ceiling on assessment increases.

The mayor's plan and Barry's proposal take into account a $16 million windfall the city expects to receive because some homes have been assessed at higher values this year. Barry previously proposed a rate reduction similar to that of the mayor, but Barry now claims his assessment exemption plan would be more effective.

The mayor asked for $201,000 for the remainder of the current fiscal year and $490,400 in fiscal 1978 to increase security at city buildings. The precautions stem directly from the takeover of the District Building and two private buildings in the city by 12 armed Hanafi Muslims last month.

The new security arrangements will add 50 persons on to the city's security guard force, the mayor said. Money also would be available to purchase metal scanners and metal detectors for some buildings.

The city already has stiffened security operations at the District Building since the takeover by doubling the number of guards at some extrances and improving the amount of equipment, including firearms, carried by the guard force.

Regarding the Metrorail operating subsidy, which is $13.6 million for the two years, the mayor said that he still favors a regional funding approach but that developing such a mechanism in the form of a commuter tax or regional tax will take time.

The 1977 request also includes $175,000 to purchase new vote-counting machines, $4.2 million for corrections and public safety and $17 million to remodel Glenn Dale Hospital.

The 1978 package includes $27.7 million for initial work on plans for a proposed $110 million convention center near Mt. Vernon Square.