President Reagan pledged yesterday to oppose any cuts in ''the current benefits'' of all Social Security recipients now on the rolls and in the 7.4 percent cost-of-living increase due this summer.

But his promise, in a letter read by Senate Finance Committee Chairman Robert J. Dole (R-Kan.) during a partisan clash at the National Commission on Social Security Reform, made no pledge to protect cost-of-living adjustments in future years for people now on the rolls, or to guarantee any specified benefit levels for those going on the rolls in the future.

In a telephone interview, Office of Management and Budget Director David A. Stockman said Reagan's letter was merely an attempt to address immediate issues and does no represent a change in position.

The national commission, created by Reagan, erupted in political conflict as Sen. Daniel Patrick Moynihan (D-N.Y.) accused the Senate Budget Committee and the administration of undermining it and foreclosing its options by ordering it to ''cut $40 billion'' from Social Security over the next three years.

''We have a crisis with the president,'' Moynihan said.

Sen. William L. Armstrong (R-Colo.)--like Moynihan, a member of both the commission and the Senate Fiance Committee--promptly accused Moynihan of ''reprehensible statements'' and ''demagoguery.''

Armstrong insisted that the resolution adopted by the Senate Budget Comittee last week merely tells the Finance Committee to come up with some way to reduce the Social Security budget deficit by $40 billion over the next fiscal three years, leaving open whether it be cuts in benefit increases, tax increases or some other way.

Senate Budget Committee Chairman Pete V. Domenici (R-N.M.), meanwhile, said he expects the $40 billion to be achieved by cutting benefit growth and adding some new tax revenues.

The conflict at the national commission foreshadows tremendous fights in Congress over the Social Security issue. The conflict will begin this week when the Senate budget resolution reaches the floor.

House Aging Committee Chairman Claude Pepper (D-Fla.), also a commission member, introduced a resolution opposing any cuts in Social Security benefits as compared with current law, guaranteeing a House fight as well.

Sen. John Heinz (R-Pa.) told the commission that he is tired of hearing all the accusations that Republicans are trying to balance the budget on the backs of Social Security recipients, and therefore will propose that Social Security be removed from the unified budget; Dole agreed.

The immediate dispute over the $40 billion proposal obscured the first apparent glimmer of agreement. Commission Chairman Alan Greenspan said a proposal by executive director Robert J. Myers to change the way the cost-of-living adjustment is figured in the future could avoid the need for periodic financing bills and make the Social Security trust funds more or less self-adjusting.

Under law, the trust funds are usually in good financial shape if wages in the economy rise at least 1.5 percent faster annually than prices; this is because the system's income flows from taxes on wages, while part of its outgo is based on consumer price rises.

Under the Myers plan, the annual cost-of-living adjustment would simply be set at 1.5 percentage points below the wage increase for the prior year, thus assuring the required relationship. Currently, it is based on the consumer price index. If wages rose 12 percent and prices 9 percent, the adjustment for the year would be 10.5 percent; if wages rose 12 percent and prices 13 percent, the adjustment would still be 10.5 percent.