The Carter administration and the steel industry have reached something of an understanding on the industry's stand on import competition: The government will begin prosecuting anti-dumping cases more aggressively, and the steelmakers will drop their push for import quotas.

Although no such agreement has been hammered out formally, that's the effect of last week's White House meeting between the industry and top government officials. The steel producers walked into the closed conference calling for stiff import quotas. They came out of it opposing them.

The turnaround was not entirely risk-free for the steelmakers. In reversing their position so quickly, they angered key congressional supporters, who had been proceeding blithely under the assumption that the industry meant what it said when it called for import restraints.

Rep. Charles A. Vanik (D-Ohio), the onetime liberal chairman of the House Ways and Means trade subcommittee who backed new steel quotas at the industry's insistence, fumed to reporters that he and other "felt betrayed."

Edgar B. Speer, chairman of the board of the U.S. Steel Corp., felt compelled to send members of the congressional steel caucus a clarifying letter assuring them the industry still was for quotas, if the anti-dumping move doesn't work.

Government and industry analysts confirmed privately that the administration had, in effect, offered the industry something of a quid pro quo. While the White House conference apparently offered the steelmakers no outright deals, sources say some points come through so clearly that officials would have been hard-pressed to miss them.

First, there were the two assertions by President Carter. The President said flatly the administration could not go along with any import quotas, for fear of undermining the current multilateral trade negotiations now going on in Geneva.

Carter also admitted that the government had been lax in enforcing anti-dumping statutes in recent years, and would now, on his order, became more aggressive. Industry officials said it was the first time in memory a chief executive had made such a strong statement.

While on one hand discouraging the push for import quotas, top administration officials almost invited industry leaders to press new dumping charges against Japanese and European producers, virtually promising them relief in any case that legally met the requirements.

And, without formally pledging specific aid, the White House held out hope of new tax breaks for the industry in the administration's coming tax-revision package. The industry also go the impression - reinforced by officials' remarks publicly - that it may see some relaxation of federal pollution-control requirements.

On that basis, it didn't take Speer long to react. Industry sources say the steelmakers had feared anyway that if the administration ever agreed to import quotas it would couple them with price restraints. The industry several times has raised prices in defiance of White House warnings.

Industry leaders insisted to reporters later they always believed that the anti-dumping actions, if acted upon aggressively, would provide more relief against imports than quotas would anyway - without as much risk of retaliation.

A recent ruling by the Treasury Department estimated that overseas steelmarkers were underpricing carbon steel here by a sizeable 32 per cent margin - the difference between what their products were selling for at home (plus transportation charges) and their prices in the U.S.

The standoff took no time to take hold. Robert S. Strauss, the President's special trade negotiator, told a conference of the Emergency Commitance yesterday that "I don't think we'll have an OMA (orderly marketing agreement, or voluntary quotas) for steel."

At the same time, Strauss added: "I think we're going to have to have some tax incentives to give stell the capital formation they need." And W. Michael Blumenthal, the Secretary of the Treasury, told reporters recently the new tax package would contain new breaks for steel.

On the other side, Barry M. Bosworth, chairman of the administration's Council on Wage and Price Stability, reiterated a conclusion yesterday in that agency's recent report saying that limiting imports would not solve the industry's problems Clearly, a truce is at hand.

The question raised by some analysts is, how long can it all last? Experts on dumping warn that even if the government presses the industry's complaints vigorously, there simply isn't enough protection in them to sustain the industry for very long.

"That's the main reason this (dumping) hasn't been used as a political solution before," one knowledgeable expert said. "You can hype the margins (and the penalties to foreign producers) for a while, but eventually they're going to win in the courts."

Meanwhile, the uneasy agreement goes on. The industry earlier this week filed two more complaints against foreign-produced strand - the fourth major petition it has filed since the administration adopted its new, more aggressive posture.

And today the Treasury is expected to announce a decision on whether to go ahead with a dumping complaint filed by the U.S. Steel Corp. against six major Japanese producers.