In a rare public disagreement, the Japanese steel industry and the government are sharply contesting an industry plan to restrict voluntarily the amount of steel products exported to the United States.

The industry's top officials are pushing the the government for a quick decision to limit sales, fearing that they face an even worse alternative in the form of anti-dumping cases brought against them by U.S. steel companies.

So far, the powerful Japanese Ministry of International Trade and Industry is refusing to join in the plan.

It is unusual for the steel industry and the government to disagree in public. They are rarely at odds on vital economic questions and normally settle quarrels in an unpublicized gentlemanly consensus. The industry solidly supports the ruling Liberal-Democratic Party, financially and otherwise.

The industry's pressure campaign went so far this week as a suggestion by Yoshihiro Inayama, president of the Japan Iron and Steel Institute, that the industry would attempt to impose its own restrictions if the government won't go along.

The idea brought resistance from the government's top steel official, Naohiro Amaya, who is director of the Ministry's Basic Industries Bureau.

Amaya said it would "not be possible" for the industry to unite in limiting exports. It would entangle them in U.S. antitrust laws and might even cause trouble under the more lenient Japanese antitrust laws, Amaya said.

President Carter's promise a week ago to vigorously enforce the U.S. anti-dumping law was the flash point that ignited the Japanese industry's almost panicky pursuit of an alternative in the form of their own voluntary restrictions.

Talking to industry and labor officials in the White House, Carter said that import quotas - even voluntary ones - were not the solution to the heavy competition from foreign steel industries.

U.S. producers have complained that the Japanese are unfairly cutting prices below production costs to sell to the American market, forcing American mills to cut back production and lay off employees.

Until Carter spoke, the Japanese industry had hopes of negotiating an orderly marketing agreement to limit their exports in the same way exports of Japanese color television sets were reduced.

The industry believes that the cards are stacked against them in an anti-dumping case, such as that brought by U.S. Steel Corp., Armco Steel, and the small Gilmore Steel. Those cases permit U.S. authorities to estimate Japanese production costs in order to determine what is a fair or unfair price.

If the dumping charges are upheld, strong penalty duties would be imposed on Japanese exports and the volume of those exports would be sharply reduced.

As a result, Japanese industry leaders one after another spent the week in news conferences and private meetings with the Ministry pressing a policy of voluntary restraints.

Nippon Steel president Eishiro Saito reportedly told the ministry that voluntary curbs are the only solution. He asked for prompt government support, apparently hoping to influence the forthcoming recommendations of a U.S. task force headed by Treasury undersecretary Anthony Solomon.

In an interview today, the ministry's Amaya said that one reason for the government's resistance is the obvious U.S. antipathy for any quantitative restrictions on trade, whether imposed or voluntary.