The Carter administration, bowing to political opposition over its already scaled-back $20 billion tax-cut proposal, agreed yesterday to back a no-frills $15 billion tax-reduction plan designed to get the measure out of committee.

In a conference with key congressional leaders, top presidential economic advisers essentially acceded to the $15 billion tax cut plan as a tactical maeuver to help break the current impasse in the House Ways and Means Committee and head off a possible cut in capital gains taxes.

The panel now is scheduled to put off any further action on the overall tax bill until after the July 4 recess - making it unlikely to resume formal markup of the legislation until mid-July.

The administration's agreement to support the $15 billion cut was conditioned on a pledge by congressional leaders to allow separate votes on a handful of the president's "tax reform" proposals when the bill reaches the floor. The two sides will negotiate over which "reforms" to bring up as floor amendments.

However, congressional experts said they doubted that the White House would be successful in winning floor approval of more than a couple of very modest "reforms." The Ways and Means panel has opposed most of the package.

The action marked the second time that the administration effectively has agreed to scale back the size of the tax cut. Carter originally proposed a $25 billion reductions, but pared that to $20 billion on May 13.

Officials stressed repeatedly that yesterday's agreement was primarily a tactical move, aimed at winning the support of a majority of the Ways and Means panel's Democrats and to head off a cut in capital gains tax. Policy makers said they hope the Senate will return the tax cut to $20 billion.

Panel leaders say they already have a coalition of Republicans and conservative Democrats willing to approve a compromise by Rep. James R. Jones (D-Okla.) that would include part of the cut in capital gains taxes.

The administration has said it is adamantly opposed to any reduction in capital gains taxes. However, panel leaders have warned the committee may scrap the tax-cut measure entirely if some compromise is not worked out.

Although Carter officially still is standing by his request for a $20 billion tax cut, several of his top advisers have been hinting recently he would not object strongly if the packages were reduced to the $15 billion level. The White House is seeking to trim the deficit to combat inflation.

The commitment to support a $15 billion tax-cut plan was made to congressional leaders by three of Carter's top economic advisers, Secretary of the Treasury W. Michael Blumenthal, presidential economist Charles L. Schultze and domestic staff chief Stuart E. Eizenstat.

On the congressional side, the participants included House Speaker Thomas P. O'Neill (D-Mass.); Rep. Al Ullman (D-Ore.), chairman of the Ways and Means panel; Rep. John Brademas (D-Ind.), the Democratic whip; and Rep. Dan Rostenkowski, (D-Ill.), a key Ways and Means member.

The $15 billion proposal essentially parallels a "no-frills" approach that liberals on the Ways and Means Committee began pushing earlier this week. The idea is to scrap all of Carter's tax "reform" proposals in order to try to muster a Democratic majority behind the bill.

In one such proposal, Rep. Joseph L. Fisher (D-Va.), a committee liberal, has suggested a flat $15 billion plan that would provide $10 billion in tax cuts for individuals and $5 billion for corporations. The personal tax cuts would be concentrated in the $15,000 to $50,000 brackets.

Meanwhile, the Treasury completed a new study showing that the average highest tax rates paid on capital gains are decidedly lower than previously thought, and that most taxpayers reporting capital gains would not be affected by the pending Jones compromise.

The survey, described by officials as the most extensive the department has conducted on the subject, shows the average marginal tax rate on capital gains was only 18.5 per cent in 1976, rather than the 49.1 per cent maximum so often cited by proponents of the compromise plan.

Moreover, the study shows that 62 per cent of all capital gains reported in 1976 were reaped by persons with adjusted gross incomes of $50,000 or less. Capital gains are the profit investors make from the sale of stocks or other assets.

The figures appeared to cast doubt on contentions by conservatives that heavy capital gains taxes ar crimping investment. Rep. William A. Steiger (R-Wis.), sponsor of the most popular bill to cut capital gains taxes, has asserted capital gains rates have risen sharply.

The Treasury study shows the average tax rate paid on all capital gains - not just those on the "margin," or the highest dollar taxed - was 15.9 per cent in 1976. The compared to 14.6 per cent in 1970 and 11.5 per cent in 1954.