The D.C. Council voted yesterday to reduce the property tax rate for homeowners by nearly 10 percent, a move that will cost the cash-strapped District more than $3 million in revenue this year and $11 million next year.

The property tax rate for homeowners was cut by 10 cents, from $1.06 to 96 cents per $100 of assessed value, in a move to offset rising property assessments.

Council members, wary of offending special interest groups in an election year, also refused to act on Mayor Marion Barry's proposals to cut city spending this year. Instead, the council told the mayor to enact the cuts unilaterally under his authority to take steps to avoid a budget deficit.

In another action aimed at relieving the city's mounting financial problems, the council gave final approval on a voice vote to a measure ending the city's policy of providing unlimited shelter and assistance to the homeless.

Despite protests by activists for the homeless, council members concluded that the policy stemming from a 1984 voter initiative had become a serious drain on the city treasury.

"This is one of the most significant pieces of legislation this government has passed," said council member H.R. Crawford (D-Ward 7), author of the measure to place limits on spending for the homeless. "The law was strangling us financially."

Advocates for the homeless warned that the council's action, overturning the so-called Initiative 17 policy, would result in thousands of homeless people being thrown out on the streets. They vowed to mount a petition drive to put the matter back on the ballot this fall.

"We're going to put it back before the voters," said activist Mitch Snyder, who led the fight for the 1984 initiative. "Folks are angry, but they're not angry at homeless people, they're angry at the government for mismanagement."

Yesterday's meeting underscored the problems facing the council in balancing concerns about a mounting deficit with a growing restlessness among middle- and upper-income voters who believe their tax bills have become excessive.

The city's fiscal woes were brought on by the soaring costs of socials programs and running a prison system, combined with declining revenue due to an economic slowdown in the region.

Barry administration officials have warned of a possible cash shortage this summer that could result in the city's missing a payroll or defaulting on its other financial obligations. The 1990 fiscal year, for which the city has budgeted $3.1 billion, ends Sept. 30.

On Monday, the administration announced a fiscal rescue package that includes a four-day furlough for about 26,000 city workers, wide ranging spending cuts and a new tax on commercial property and public utilities.

The mayor can order the furlough on his own, but he asked the council to approve new taxes, as well as going along with the spending reductions in such areas as AIDS spending, job training, summer youth programs and the recreation department.

The mayor submitted the cuts, totaling $33 million, to the council as part of a supplemental 1990 budget, but the council effectively killed the plan by refusing, on a voice vote, to set the matter down for a public hearing next week.

Council member John A. Wilson (D-Ward 2), chairman of the Finance and Revenue Committee, said it is the mayor's responsibility to live within the budget passed by the council in March. He said Barry has the authority under the home rule charter to order recissions in agency budgets to avoid a deficit.

Wilson and other council members, most of whom are running for reelection or seeking higher office, also said they would not go along with Barry's tax proposals.

"I'm trying to force people to do what they're supposed to do -- their job," Wilson said. "Don't they have a responsibility to live within the budget?"

Council Chairman David A. Clarke (D) and member Charlene Drew Jarvis (D-Ward 4) dissented from the council's action on the supplemental budget request, saying that members had a responsibility to act on the matter themselves.

City budget director Richard C. Siegel accused council members of abdicating their "authority to act," and said the mayor does not have the authority to order budget cuts in the court system and other independent agencies without council approval.

"Saying it is up to the mayor is a weak excuse for inaction," Siegel said. "They have authority. All they have to do is exercise it."

While the council rejected the mayor's budget plan, they gave him the green light on his proposal to furlough city workers in August. Council members Nadine P. Winter (D-Ward 6) and Wilhelmina Rolark (D-Ward 8) offered an emergency bill to limit the mayor's authority to furlough lower-grade city employees.

Winter and Rolark said their bill was designed to prevent low-income workers from being harmed, but other members -- including Wilson, William Lightfoot (I-At Large) and Frank Smith Jr. (D-Ward 1) -- said it was unfair to tie the mayor's hands when the council was unwilling to approve new taxes.

Members voted 7 to 5 to back the measure, but the bill failed because it did not gain the two-thirds support needed to pass an emergency bill that would take immediate effect.

The council action on the homeless, expected to take effect in late September or early October, requires homeless people receiving shelter and who have jobs or public assistance to pay up to 30 percent of their income into an escrow account to help them find permanent housing. It also limits the amount of time that homeless people can stay in shelters, among other provisions.

One portion of the measure that takes effect immediately would eliminate the provision of Initiative 17 holding that homeless people are entitled to emergency shelter. Council members said that was necessary so that the city no longer would have to pay about $5,000 a day in court-imposed fines for failing to abide by the right-to-shelter law.

However, advocates for the homeless said yesterday they would challenge that in court.

Staff writer Nathan McCall contributed to this report.