The chairman of the House Ways and Means Trade Subcommittee asked President Carter yesterday to consider a seven-point program to help the ailing steel industry - including negotiated import quotas and a series of sizeable tax breaks.

Rep. Charles A. Vanik (D-Ohio), said the actions were neded to stimulate expansion of steel making capacity and bring the industry back to health. He asserted the package would be "better for" the economy than a $15-to-$20 billion general tax cut.

Vanik's proposals, outlined in a letter to Carter, also include faster action on industry anti-dumping cases, a stretchout of current anti-pollution requirements, an easing of antitrust laws, and a promise not to review last year's quota agreement on specially steel.

There was no immediate reaction from the White House. A special administration task force under Anthony M. Solomon, undersecretary of the Treasury for monetary affairs, is studying the steel question and trying to put together an administration proposal.

However, Charles L. Schultze, chairman of the Council of Economic Advisers, yesterday again rejected the use of protectionist measures such as quotas, saying the industry's problems stemmed from a variety of factors, not just import competition.

Schultze told a press conference in Detroit, "In my judgment, the government should not prop up the steel industry." He said, "The answer has to come in terms of a healthy economy, not protectionism."

Steel industry sources were lukewarm to the Vanik proposals. One official said the quotas suggested by the chairman were so far above existing import levels that they actually would allow more foreign-made steel to come into the U.S.

The series of developments followed a decision by the Treasury on Monday that five Japanese steel companies have been selling their products here below their actual production costs - the first time in recent history that the industry has won a "dumping" case.

Robert S. Strauss, the President's special trade negotiator, has been encouraging steel makers to file such charges in lieu of seeking protectionist measures, but the industry has complained that the procedure is too long and unwielding.

The Vanik package, made public by the congressman's office yesterday, includes these elements:

Immediate negotiations to persuade European, Japanese and other steel makers to limit their exports here voluntarily to a combined 18 per cent of the total U.S. market, divided equally among each of the three sectors.

The agreements would be accompanied by an anti-inflation provision that would automatically raise the level of imports allowed by another 10 to 15 per cent for two years whenever U.S. steel makers raised their prices "inordinately." That word was not defined.

Faster depreciation rules to allow steel companies to write off the costs of their plant and equipment more rapidly. Vanik proposed shortening existing guidelines to provide for a 13-year-period instead of the present 18 years.

A "stretchout" of current government pollution control requirements to allow the industry to take longer to comply with them. Vanik gave no specific suggestions.

More favorable tax treatment to enable steel firms to deduct the cost of pollution control equipment as a regular business expense the same year the money is spent.

Faster handling of industry antidumping petitions, which now often take a year or more before relief finally is granted.

Amendment of antitrust laws to allow individual steel firms to make formal agreements to divide up production of portions of a product market to hold their facilities to an economical size.

A promise by the President not to carry out his threat to "review" the 1976 quota agreements on specialty steel. Those agreements originally were to last for three years, but the White House ordered a restudy after the industry defied the President in increasing its prices.

Vanik claimed in proposing these measurers that the package could spur investment in new steel making facilities by $15 billion to $20 billion. He offered no supporting documents estimating the impact of the proposals on imprts or on consumers.

Steel industry sources estimated that Vanik's proposal for voluntary import quotas would allow entry of 19 million tons of foreign-produced steel into the U.S. each year. That compares with an estimated 17 to 18 million tons this year, and a cutback to 12 million tons sought by the industry.

Apart form the import levels and the anti-inflation trigger, the Vanik package appears to include virtually all the major relief actions the industry has sought in recent years. Most of these have been rejected by one administration or another.

The advent of increasing layoffs in Amrican steel manufacturing plants has led to new concern in Congress. However, Rep. Charles J. Carney (D-Ohio) chairman of the newly-formed "steel caucus" in the House ,predicted that no congressional action would be likely until early next session.