House Republican leaders yesterday proposed as a cost-cutting step that the Social Security retirement age be raised in stages from 65 to 68 begining in 1990.

They also proposed that a check be placed on future benefits so they would not rise as fast as under current law - and also would rise a little slower than President Carter has proposed in his Social Security recommendations.

In addition, the Republicans suggested a phase-out of the restriction the amount a Social Security recipient can earn. They would lift the amount to $5,000 next year and have it disppear by 1980.

The GOP leaders offered their proposals as alternatives to set that Carter put forward earlier this year to shore up the financially ailing Social Security system, which now makes up a fifth of the federal budget and helps support one out of every seven Americans.

Where Carter put heaviest emphasis on additions to Social Security revenue, the Republicans put heavy stress on cutting costs.

A House Ways and Means subcommittee will start marking up Social Security legislation next week.

The 15-point GOP plan includes a three-stage increase in the Social Security tax rate, starting in 1982 and totalling 1.2 per cent each for employers and employees. It also would provide improved payments for future women beneficiaries and steps to reduce the impact of "double-dipping" by government employees who are simultaneously collecting federal pensions and some Social Security benefits. The federal retirement system would eventually be integrated with Social Security.

Ranking Ways and Means Republican Barber B. Conable Jr. (N.Y.), outlining the proposals at a news conference with GOP leader John J. Rhodes (Ariz.) and others, called them a "realistic" plan that would save the Social Security system from running out of money and without dipping into general treasury income-tax revenues or removing the ceiling on a worker's wages for which his or her employer must pay Social Security taxes.

Both these new methods of financing have been suggested by Carter, but yesterday Conable, Rep. Bill Archer (Tex.) and other Republicans roundly denounced them and said they would destroy the insurance character of the system, paid for by earmarked taxes, and make it into a welfare system.

The Republican proposal was quickly denounced by Health, Education and Welfare Secretary Joseph A. Califano Jr., who called it an attempt to solve fiscal deficiencies in the system by cutting future benefit growth and loading more taxes on low-and-middle-income workers.

Califano said the GOP proposal "shatters the solemn promise of the dfederal government to the American people by reducing by 6 percent the retirement benefits," they would receive under Carter's plan "and by eventually denying full Social Security payments until age 68 instead of the present age 65."

Conable argues, however, that the administration plan, by proposing to rely on higher taxes on business and on the income tax, was an unrealistic "lick and a promise, a mile wide and an inch thin."

He said problems of the Social Security system, bedeviled by reduced revenues because of unemployment and a higher proportion of older people in the population than heretofore, could not be solved without some brake on the growth of future benefits.

While cutting back the general level of future benefits below what the Carter administration is contemplating and lifting the retirement age to 68, the GOP plan also includes some politically attractive and relatively low cost benefit improvement.

They includes:

Removal of the $3,000 earnings limit for beneficiaries.

An extra 25 percent in benefits for a working wife provided her total as a result did not exceed the general benefit ceiling; a reduction from 20 years to five years in the length of marriage eligibility test for a benefit for the husband or wife of an insured worker; allowing widows and other beneficiaries who remarry to avoid loss of reduction of payments. All these would apply only to future retirees.

Under a law passed in 1972, benefits rise each year with inflation. But the law overcompensated for inflation, so that without new legislation some people in the future could retire on benefits higher than their pre-retirement earnings.

Both the administration and GOP plans propose to rewrite the 1972 formula to put a brake on this calculation.

In doing so, the administration wants future retirees to end up with monthly benefits of about 45 per cent of their normal Social Security-covered earnings in the year before retirement (about the current ratio).

The GOP plan proposes around 42.5 per cent, Conable said, but this would phase in so that no one would get less than a person of the same covered earnigns who retired earlier. The Republicans said this did not mean a cutback of current levels, but merely a slightly lower growth of benefits. And money would be saved.

The percentages sound small but when computed in system with more than $100 billion annual benefits over many years, the savings could be huge.

The GOP plan also proposes to increase the basic retirement age to 68 in stages from 1990 to 2001. A worker could still retire earlier but with a reduced level of benefits. The Republicans conceded this was, in effect, a benefit reduction.

"The proposal" they said, doesn't offer "something for nothing." But Sen. Gaylord Nelson (D-Wis.), chairman of the Senate Social Security Subcommittee, said the age-68 plan "won't fly."

The Republican plan also calls for a slight reduction in future disability benefits in a small number of cases; would divert three-quarters of a scheduled Medicare tax rate increase to the old-age and disability trust funds to help them until 1982, would freeze the minimum Social Security benefit for a government employee who is also collecting a federal employee pension; would put government employees under Social Security but without loss of any federal employee benefits earned till now (details are to be worked out.)

The 1.2 percent tax increase (the current rate is 5.85 per cent on employers and employees) would come as follows: a half per cent in 1982, three-tenths in 1990 and four-tenths in 2000.