The Carter administration will ask Congress today to change the way the government calculates cost-of-living increases for Social Security, veterans retirement and other pension programs -- a move that could cost recipients billions in potential benefits.

The proposal, expected to be included in the administration's fiscal 1982 budget proposals, will seek to compute these annaul increases using a modified form of the consumer price index that omits mortgage interest rates.

Analysts estimated that if the new plan were in effect today it would trim the annual inflation adjustments for these benefits by a combined $4 billion, simultaneously reducing the budget deficit by that amount.

The change would affect cost-of-living adjustments for 14 major and minor federal benefits programs, from civilian retirement and disability benefits to coal miners' disability programs.

Analysts stressed that a shift to the new measure would not affect the current CPI, which the Labor Department would continue to publish as it has regularly for decades.

The decision, approved by President Carter earlier this month, was disclosed at a news conference by Labor Secretary F. Ray Marshall, who opposed the change but was overruled by the Office of Management and Budget.

The shift proposed by the administration has long been considered by White House and congressional budget-cutters, but even the suggestion of such changes in the past has run into substantial opposition on Capitol Hill. s

It was not immediately clear whether the incoming Reagan administration would endorse the Carter proposal. However, key Reagan aides have endorsed the concept in the past and were regarded as unlikely to try to block it now.

Economists are virtually unanimous in agreeing that the current procedure of using the full consumer price index to adjust these benefits results in an artificially bloated increase for recipients.

The reason is that the CPI, as the index is known, samples home mortgage interest rates every month and thereby exaggerates the impact of these charges on actual family living costs.

Economists point out that most families don't feel the impact of higher mortgage rates unless they actually buy a house during the month the index is compiled.

When mortgage rates were soaring last winter and spring, the surge helped bloat the CPI by as much as 2 percentage points above what it otherwise would have been and added substantially to cost-of-living raises based on the index.

The measure the administration is proposing to use would disregard all changes in mortgage interest rates and count instead of a specially calculated "rent" substitute that would measure the actual cost of obtaining shelter.

Economists say this version of the index, already being complied regularly by the Labor Department, would have shown a 10.9 percent inflation rate for the year ended last November, compared with 12.6 percent for the full CPI.