The Reagan administration said yesterday it is investigating steelmakers and importers in 12 countries, including the mammoth Mitsui Trading Co., on 40 separate fraud charges connected with their imports here. It also has initiated three steel anti-dumping cases against Japan, Korea and Yugoslavia.

Federal grand juries around the country are investigating allegations of fraud connected with steel imports and a grand jury investigating Mitsui may have a decision within 30 days, Commerce Undersecretary Lionel Olmer told reporters in Tokyo.

The government also will review alloy steel imports from West Germany and Austria to determine whether an antidumping investigation is warranted, and 11 other antidumping or countervailing duty cases may be started, Commerce Secretary Malcolm Baldrige said.

Baldrige briefed reporters about the investigations in a hastily called press briefing following announcement by Olmer ion Tokyo of the fraud investigations. Baldrige denied that the massive antidumping activity was an effort to get tough with European steelmakers, who American companies claim have been unfairly subsidized by their governments. The antidumping investigations are the first ever initiated by Commerce since it received jurisdiction in those cases in January 1980.

Olmer said the investigations are part of the administration's decision to show steel importers "we mean business."

"It's not a question of getting tough on someone," Baldrige said. "It's a matter of doing our job."

The nation's largest steelmaker, U.S. Steel, last year alleged that the government wasn't doing its job of monitoring unfairly priced foreign steel, and this led to one of the nation's largest trade cases in history.U.S. Steel filed antidumping complaints against steelmakers in seven European countries.

The case was withdrawn when the Carter administration made changes in the trigger price mechanism, a system designed to start an investigation automatically when foreign steel is believed to be dumped, that is, imported here at prices below its fair value.

In the fraud cases, the government is investigating charges that the steelmakers and importers falsely described merchandise, double-invoiced, filed false damage claims and used false terms of payment to disguise true costs and prices in circumventing the trigger price mechanism, Baldrige said.

Several of the cases already have been presented to grand juries, but Baldrige would not say where the grand juries were meeting, how many there were or what companies are involved other than Mitsui. The Mitsui case has been publicized in investigations on the West Coast, Baldrige said.

"We're probably seeing some more violations [of the trigger price mechanism] than we have in the past, perhaps because of the currency changes" that have resulted in cheaper imports, Baldrige said. "But there's no wholesale attempt to challenge the TPM system."

Baldrige said Commerce will determine whether the recent strength of the dollar relative to the yen and European currencies is a valid reason for the low-priced imports.

Commerce's antidumping investigations are of imports of nails from Japan, the Republic of Korea and Yugoslavia which amounted to $46 million last year, about 25 percent of domestic market sales. From Oct. 21, 1980, to March 31, all nails from Yugoslavia, 44 percent from Japan and 99 percent from Korea were imported below the trigger prices, the Commerce Department said.

The department also is reviewing whether to initiate an investigation against steelmakers in West Germany and Austria. Commerce found during the first quarter of this year the percentage of alloy tool steel imports from West Germany tripled and those from Austria more than doubled compared with the same period last year.

Commerce also is preparing to begin audits of U.S. steel importers to determine whether the trigger price mechanism is being circumvented by sales through chains of related parties, Baldrige said.

Olmer said Japanese producers were worried that the administration intended to give preclearance to European producers, allowing them to sell steel here below trigger prices after showing they can legally produce steel at low costs. Baldrige said 11 or 12 foreign steel producers have asked for preclearance, and perhaps about half of them will get it.