President-elect Ronald Reagan was urged yesterday by his task force on the cities to end the government's housing programs for the poor and instead provide persons in low-income households with vouchers so they could live where they choose.

The advisers also proposed phasing out the multibillion-dollar "public sector" jobs program, saying it has been a failure and should be replaced by tax breaks and other incentives to businesses to train and hire persons out of work.

"I don't expect this will be wildly popular among liberals," said San Diego Mayor Pete Wilson, who headed the 19-member task force, which included a heavy sprinkling of conservative academics. "After billions spent for [public service jobs], we still have massive unemployment. The good intentions of [Great Society programs] are not enough."

Later, another urban advisory group to Reagan, also headed by Wilson but including mostly Republican mayors from Sun Belt cities, announced that they had recommended to the president-elect's transition team that Richard Carter, the mayor of Peoria, Ill., be named secretary of the Department of Housing and Urban Development. That group also said it believed mayors should be appointed to head the Department of Transportation, the Environmental Protection Agency and the Department of Health and Human Services, though they did not submit names for those positions.

The idea of providing housing vouchers for the poor instead of having the federal government build or subsidize specific apartments for them has been kicked around for more than a decade. Proponents claim vouchers would cost less than public housing and rent supplement programs, would provide more choice and would mitigate against large residential concentrations of poor people.

Resistance to vouchers has stemmed from a fear that they would lead to further inflation in the rental housing market -- burdening both the middle class and the unsubsidized poor -- and might not work effectively without other efforts to counter racial discrimination.

HUD has been experimenting with various housing allowance programs in 12 cities since the early seventies. A study of those programs by Massachusetts Institute of Technology Prof. Bernard J. Frieden concluded that they had worked for the most part -- there was no indication that they have led to inflation in the rental market although blacks and Hispanics did appear to encounter some discrimination in some cities when they attempted to use the allowances to move to better housing out of the ghetto.

Mayor Wilson said he believed that a voucher system would be more expensive than existing programs initially but that there would be substantial savings in the long run. He acknowledged that it might be difficult to sell the idea to Reagan administration budget-cutters.

Carver, 42, the president of a lumber and building supply company and the mayor of Peoria since 1973, is popular among both Republican and Democratic mayors.The president until last June of the U.S. Conference of Mayors and still a prominent member of its leadership group, he has been in and out of Washington since the election and would clearly like to be named HUD secretary. On Friday, Gary, Ind., Mayor Richard Hatcher, San Francisco Mayor Dianne Feinstein and Nashville Mayor Richard Fulton, all Democrats, said they had recommended to the Reagan transition team that Carver get the housing job.

Yesterday Carver had meetings with James Baker, Reagan's designated White House chief of staff, and Sen. Jake Garn (R-Utah), the chairman-to-be of the Senate Banking and Housing Committee, which will handle the confirmation of Reagan's nominee for HUD secretary.