The D.C. City Council tentatively approved yesterday spending $5 million this year to maintain present levels of welfare payments for 3,500 "working poor" families who otherwise would have been removed from public assistance by new Reagan administration guidelines.

The measure immediately ran afoul of Mayor Marion Barry, whose budget experts insist the city doesn't have enough money to pick up the additional welfare costs.

Barry said through a spokesman that although he opposed Reagan's cuts in funds for low-income families struggling to gain financial independence, "The council should not use fiscal mirrors in making its decisions."

But several council members said that it was Barry who had played political games with the budget -- games that have enabled Barry to "discover" additional funds for pet projects and politically important contract negotiations.

"I'll bet you that in the next few weeks there will be a lot of reopenings of contracts with city employes, and there will be plenty of money for that," said City Council Chairman Arrington Dixon. "But the working poor can't get support."

The decision on welfare funding capped a frequently wrangling, five-hour session at which the Council:

Approved measures that would increase the annual motor vehicle inspection fee from $3 to $5 beginning March 31. The inspection fee, which is paid as part of motor vehicle registration, was last raised in 1969.

Passed a proposal that would require persons who drive automobiles with out-of-state tags -- about 20,000 people, by city estimates -- to purchase $25 reciprocity stickers within 30 days of moving to the city.

Upheld by a vote of 10 to 2 with one abstention, a controversial redistricting plan that would move most of Georgetown from Ward 3, the affluent area of town west of Rock Creek Park, to Ward 2, in the central city.

Moments earlier, the council had rejected a substitute plan, offered by Ward 2 council member John A. Wilson, that would have moved parts of Adams Morgan south of Florida Avenue NW between 18th Street and 14th Street NW from Ward 1 to Ward 2.

The substitute plan also would have transferred into Ward 1 a section of Ward 3 east of Connecticut Avenue NW directly north of the National Zoo.

Wilson said that many community leaders from the poorer section of his ward were opposed to the addition of about 10,300 voters from wealthy Georgetown.

"I don't want the people of Georgetown in my district," Wilson said. "I don't think the majority of people in my district want them."

More than 95 percent of the working-parent households in Washington whose incomes are supplemented by welfare payments stood to lose an average of $143 in monthly benefits because of cutbacks in federal matching funds for that program.

The measure to avert those cuts, which would make the District of Columbia the first major jurisdiction to foot the entire cost of that program, was sponsored by council member David A. Clarke (D-Ward 1).

Clarke's proposal was approved as a rider to a bill to bring the city's AFDC program in line with new, tougher federal guidelines for determining recipients' eligibility and reducing administrative mistakes and client fraud that have greatly added to the cost of the program.

The council and mayor previously had avoided other welfare cuts by approving expenditure of about $1.4 million to pay welfare benefits for 18- to 20-year-olds who attend school and for needy women who are pregnant with their first child -- two categories of recipients who also would have been eliminated under new Reagan guidelines.

But Barry's aides have insisted that there isn't enough money in the current fiscal 1982 budget to continue welfare payments to working poor families, as the council voted to do yesterday.

"Even if we could find funds in Fiscal Year 1982, the incremental costs in 1983 and beyond would create an impossible strain on the District budget without federal aid," City Administrator Elijah B. Rogers said this week in a memorandum to a council member.

The passage of the bill requiring motorists to buy reciprocity stickers was aimed at cracking down on a problem that has been an irritant to D.C. transportation officials for years.

Under the proposal, the $25 reciprocity stickers would be valid for only six months, after which the motorist would have to pay the average $52 cost of registering in the city and buying D.C. tags. Council staff members estimated the plan would raise about $100,000 for the city government, but D.C. Transportation Director Downes said it could be as much as $1 million if fully enforced.

In other action yesterday, the council tentatively approved a measure that would sharply increase the size of the mayor's and council members' constituent service funds.

Under the proposal, the mayor and council members would be able to collect $25,000 in constituent service funds in one year with a maximum contribution of $200 from any one source.

Currently, the mayor and at-large council members can collect $20,000, with a maximum $100 from individual contributors, while ward members can collect $10,000 with a maximum $50 from individual contributors.