House Republicans yesterday unveiled a proposed job-training and employment program for mothers on welfare, saying it would cost less and help more women find jobs than a Democratic plan approved by the House Ways and Means Committee.

The Republican alternative, developed by a task force headed by Rep. Hank Brown (R-Colo.), will be offered as a substitute when the Democratic measure, passed by the committee in June, reaches the floor. House Minority Leader Robert H. Michel (R-Ill.), who will be chief sponsor, said President Reagan told him yesterday that "we have his full endorsement." The president himself later endorsed the bill.

Brown said the Republican plan would cost the federal government $1.4 billion over five years, compared with $5.3 billion for the Ways and Means bill and $2.3 billion for a plan proposed by Sen. Daniel Patrick Moynihan (D-N.Y.).

All three proposals require the states, for the first time, to set up work, job-training and other programs to help parents shift from the Aid to Families With Dependent Children welfare rolls to payrolls.

Brown contended the GOP proposal would be the most effective, in part because it mandates that at least 70 percent of eligible mothers participate in training programs after nine years.

But he said the principal advantage of the Republican proposal over the Democratic bills is that "its primary purpose is not to increase benefits," which Republicans believe is more likely to encourage people to stay on welfare.

"If you increase welfare benefits you ensure that people will stay on welfare," said Rep. John G. Rowland (R-Conn.), a task force member.

Rep. Bill Frenzel (R-Minn.) said the Ways and Means bill undermines its basic aim of getting people off welfare because it includes benefit increases and other provisions that discourage work. He said the bill would encourage people to stay on welfare because it: Requires that all states provide AFDC benefits to families where the father is present but unemployed (about half now do).

Provides higher federal reimbursement rates to states that raise benefits.

Allows welfare clients to refuse minimum-wage jobs if current pay scales for those jobs are higher.

Permits a welfare client to turn down a job if it results in a net loss of income including the value of food stamps and Medicaid.

None of these are in the Republican substitute.

Under the GOP bill, total federal appropriations for the training and placement programs, plus costs of necessary child care, would be limited to $500 million for the first year, and after that, to such sums as Congress appropriates. The money would be used to reimburse the states for about 79 percent of the first $200 million a year they spend on the new programs, and 50 percent above that.

The Ways and Means bill places no limit on federal outlays.