More than three dozen women's and public-interest groups attacked the Reagan administration's budget yesterday, charging that proposed cuts would erase years of gains made by women.

"Women recognize that a serious economic condition exists, and we agree with the critical need to reduce inflation, lower unemployment, increase productivity and reduce the tax burden," said Iris Mitgang, chairman of the National Women's Political Caucus. "But this must be accomplished through an economically sound policy that is also compassionate and fair. The Reagan proposal is neither."

Under the auspices of the National Women's Political Caucus, the coalition began a Capitol Hill lobbying effort in an attempt to reverse the proposals. The coalition sent to Budget Committee members of both houses, and other key members of Congress, copies of position papers detailing what it claimed would be the budget reductions' negative impact on women.

"The National Advisory Council on Economic Opportunity has estimated that by the year 2000, virtually 100 percent of the poor will be women-headed households," the women said in a statement. "We are deeply concerned about a national fiscal policy that will lock women into the cycle of poverty and offer no relief for the future."

The coalition charged that reductions in such programs as Aid to Families with Dependent Children, the Comprehensive Employment and Training Act and the Legal Services Corp. would have harsh results on women.

Ninety percent of all single-parent families are headed by women, the caucus said, with more than one third earning incomes below the poverty line, even with public assistance.

The coalition predicted dire effects in health and education and said that the administration proposal to consolidate many programs into a few block grants to the state and local levels would "virtually end the only federal support in critical areas."