Leaders of the nation's steel industry, which is suffering from increasing unemployment and slow sales, said yesterday that they expect no recovery in their business until possibly the end of the year.

Despite their poor prospects, the leaders reaffirmed their faith in the Reagan administration's policies and said government officials on the trade front are vigorously enforcing trade laws, although they said foreign steel makers continue to undercut them unfairly.

"We're not predicting much growth this year, D.S. Arnot, executive vice president of Bethlehem Steel Corp., said before the American Iron and Steel Institute's 90th annual general meeting here. He predicted that the industry will show no major growth until next year.

The industry executives, complaining of a sluggish economy, alleged unfair competition from imports and government environmental regulations, seemed to doubt administration predictions of economic recovery this summer. They said that they expect more layoffs, operating losses and possible closure of steel facilities.

The industry's recovery will be led by consumer purchases of automobiles and other products that cannot take place until the federal budget deficit problem is resolved and interest rates come down, Arnot said.

"Hopefully we have bottomed out," Arnot said. "It's not going to get that much better faster."

"I hope we're near the bottom" of the recession, Bethlehem Steel Chairman Donald H. Trautlein said in an interview. But he added, "We still support the objectives of the Reagan administration."

National Steel Corp. Chairman Howard Love described the state of the steel industry as "grim" and "bleak" and said that "its fortunes are tied very much to the whole economy. The health of the automotive, machinery, appliance, capital goods, construction and equipment industries is reflected in their demand for steel and consequently in our production schedules, and you know what has happened to those industries, largely as a result of high interest rates," Love said.

U.S. Steel Corp. Chairman David M. Roderick said he doesn't expect much growth in the industry until imports--which captured about one-fourth of the U.S. carbon-steel market this year--are slowed. The trade problem "is serious, it is worsening, and it won't disappear by benign neglect," Roderick said.

However, Roderick later said the "benign neglect" comment hadn't been aimed at the Reagan administration. He said the administration had been "slow and indecisive" at first in responding to the sale of unfairly subsidized imports.

However, he added, "I would not say we have benign neglect at the moment."

Both Roderick and Republic Steel Corp. Vice President William J. Williams said their companies are considering filing more complaints against foreign steel producers of unfair trade practices, but they didn't say against whom those complaints would be made. The steel industry already has filed 55 complaints against foreign steel makers, and the Commerce Department has planned to make preliminary decisions on some of those cases on June 10.

Trautlein said he didn't expect any major layoffs at the Sparrows Point plant in Baltimore, at least for the next four to six weeks. However, he said the more than $300 million in modernization planned there could be affected if the Commerce Department finds little evidence of unfair subsidies received by foreign steel makers next month.