The House subcommittee on public assistance yesterday approved a bill that would help reduce next year's deficit but also, in an effort to combat effects of the prolonged recession, provide an extra 13 weeks of unemployment benefits to workers who exhaust their initial 39 weeks.

Up to 600,000 workers in 29 states with high unemployment would receive the extra benefits, Labor Department officials said. They said it appeared workers in the District of Columbia and Virginia would not be eligible because unemployment is not high enough, but Maryland workers might.

To help offset the extra costs of this and several other liberalizations of welfare benefits it also approved, the Democratic-dominated subcommittee recommended an increase in income taxes on individuals who collect unemployment benefits part of a year then find jobs and end up with substantial earnings.

At present, unemployment benefits are taxable only to the extent they lift an individual's income over $20,000 or a couple's over $25,000. These thresholds would be reduced to $12,000 and $18,000.

The extra 13-week program, which would be in effect until Sept. 30, 1983, would cost $562 million in fiscal year 1983.

The assortment of program cuts and tax increases was voted to comply with the deficit reduction instructions in the budget resolution Congress adopted last month. As steered through the subcommittee by Chairman Harold E. Ford (D-Tenn.), they would cut net federal outlays for welfare and unemployment programs by about $2.6 billion over the next three years compared with current cost projections.

The subcommittee made only a handful of cuts in programs and turned back Republican proposals to cut more; the tax increase on unemployment benefits would produce nearly $2 billion of the overall reduction.

The new 13-week program and the added tax are expected to have easy sailing in the parent Ways and Means Committee today, since the panel endorsed a similar proposal earlier this year.

The $2.6 billion in net reductions more than met the subcommittee's budget reduction targets in the welfare area. But for all the programs in its jurisdiction, medical as well as welfare, Ways and Means is far short of its $13.75 billion target for the next three years.

So far, the Medicare cuts recommended by the Ways and Means health subcommittee come to $5.9 billion or perhaps less (the impact of one provision is unclear). With the welfare and unemployment votes, the full committee still has another $5.2 billion to go.

In dealing with welfare, the subcommittee voted to reverse some of the cuts made last year at the president's request. It voted to require welfare agencies, when computing benfits for a welfare client, to disregard the first $50 a month in family earnings (the present figure is $30), up to $175 a month in work expenses (Congress cut it to $75 last year) and one third of remaining income, without the four-month time limit imposed last year.

It also agreed to repeal a provision barring families from welfare if their gross income exceeds 150 percent of the "needs standard" set by the state.