The House Ways and Means Committee yesterday approved the most sweeping overhaul in a generation of the nation's welfare program for low-income parents with dependent children.

The bill would require states, for the first time, to establish large-scale programs involving mandatory job training, education and work and designed to shift recipients from Aid to Families with Dependent Children (AFDC) welfare rolls to private payrolls.

Although President Reagan put welfare changes on the national agenda with a dramatic statement in his 1985 State of the Union message, the committee's 13 Republicans opposed it. All 23 Democrats voted in favor.

While many Republican members said they like the thrust but not the details of the bill's education, training and work provisions, they and the Reagan administration strong oppose its benefit increases.

This opposition, shared by many Senate conservatives, portends difficulty on the House and Senate floors and a possible veto.

The bill's cost over the next five years is estimated at $5.2 billion, about $1.1 billion of which would cover job training, education and work provisions.

Rep. Hank Brown (Colo.), senior Republican on the panel's public assistance subcommittee, called the bill "a disgrace," saying that, by "jacking up welfare benefits to where they exceed pay for entry-level jobs," it would discourage people from leaving welfare, undermining the work provisions.

But subcommittee Chairman Thomas J. Downey (D-N.Y.) called the bill "an important first step . . . to help a poor family move away from welfare to work."

In raising benefits, he said, "Democrats look at poor children" and how their development is affected by poverty, split families and lack of education and training. One-fifth of American children under 18 are in poor families.

Downey cited a provision opposed by Republicans. It would require states to extend benefits to families with a father in the home who cannot find a job. Half of the states do not provide benefits to such families.

The provision, he said, "ends the incredible policy of not paying benefits to children because parents decide to be together." It would take effect Jan. 1, 1990, and cost about $1.1 billion over five years.

The bill's proponets also said another major provision, which would raise federal reimbursements to the states by 25 percent for any benefit increases made after September 1988, would induce states to raise benefits. This provision would cost $1.2 billion over five years.

The federal government now reimburses a state 50 to 78 percent of its benefit costs, with poor states receiving the higher match. These rates would be raised 25 percent on benefit increases, but the overall match could not exceed 90 percent.

As of last January, the maximum AFDC benefit in the typical state was about half of the poverty line for a family of three.

House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) said the bill "builds on the experience of the states, including my own . . . which have developed work, education and training programs."

Welfare parents with no children under age 3 would be required to participate in work or training programs, and those with none under 1 could be included in them under certain conditions.

About 3.8 million welfare parents, mostly mothers, and about 7 million children are enrolled in the AFDC program. Very few of the parents are employed.

It is estimated that at least 75,000 such parents annually would participate at first. The federal government would pay 65 percent of the costs of the work and training programs.

States would be required to provide or pay for child care as needed.

The bill also would allow people to continue receiving child-care aid and Medicaid benefits for six months after working their way off welfare.

The bill also provides that, as an inducement to work, computation of welfare benefits -- starting Oct. 1, 1988 -- would not include the first $100 of monthly earnings plus 25 percent of the remaining earnings of a welfare client who works but still has low income.

The National Governors' Association and the American Public Welfare Association praised the bill.