The reported slashing of the Department of Housing and Urban Development's major program for low-income housing does not signal a rejection of HUD Secretary Samuel R. Pierce Jr.'s voucher program, a department spokeswoman said today.

Pierce, in Houston to speak at a homebuilder's convention, touted the vouchers as the "centerpiece" of assistance programs for poor Americans, just two days before it was reported that funds for the vouchers had been virtually eliminated from the Reagan administration's fiscal 1986 budget.

HUD sought funds for 100,000 housing vouchers but received money for only 3,500 in the budget the administration will send to Congress next week, according to documents obtained by The Washington Post.

Housing vouchers will be given to low-income families, who can then shop for their own homes or apartments and use the vouchers to help pay rent. Families pay 30 percent of their income for rent and HUD will make up the difference between that amount and the fair market rent.

If the administration sliced voucher funds, the move "was not a withdrawal of the commitment to vouchers. We are fully convinced that vouchers are the way to go," said June Koch, HUD assistant secretary for policy development and research. Koch said she could not comment on the budget, adding that she would say only that "if" full implementation of the program was "put off," it was for budget reasons only.

Pierce said in Houston that HUD's "objective is to have the vouchers as the centerpiece of the program and then have a rehabilitation of existing housing program and a small building program. We think that is the way to go and that we can house more people less expensively to the government and bring our housing debt down."

The present section 8 rental assistance program "is really a forerunner" of vouchers and will be replaced by them, he said. Unlike the requirements for vouchers, section 8 rules limited landlords to rent levels set by HUD.

Congress approved funds in late 1983 for demonstrations, or trials, of the vouchers in more than 20 cities and states. The demonstrations have not gotten under way yet.