A day after the Senate passed its trade bill, Majority Leader Robert C. Byrd (D-W.Va.) yesterday called on House Speaker Jim Wright (D-Tex.) to begin planning for a crucial House-Senate conference that will have to steer a narrow line between congressional pressure for a tough law and the White House threat to veto a bill it finds objectionable.

The conference, expected to be one of the most complex ever, involving as many as nine House and Senate committees, is not likely to start until after Labor Day, when Congress returns from its August recess.

But trade specialists on the staffs of the Senate Finance and House Ways and Means committees, which have primary jurisdiction over the major parts of the trade bill, are expected to begin preliminary work early next month to define areas of agreement.

There is likely to be one main conference with a number of subgroups focusing on provisions of the legislation that go beyond the jurisdiction of the committees that traditionally handle trade legislation.

The Senate Labor Committee, for instance, reported one of the most controversial provisions of the Senate bill, an amendment that requires big companies to give advance notice of plant closings or mass layoffs that involve more than 100 workers, but there is no similar provision in the House measure. Similarly, the Senate refused to include a measure that the House passed on the recommendation of its Banking Committee that requires registration of foreign business and real estate purchases. Both of those items are considered veto bait by the administration.

Nonetheless, U.S. trade officials pointed out that the House and Senate bills are complementary, with none of the provisions that the White House finds most objectionable contained in both measures. This makes it easier for the conference to modify the most objectionable procedures to avoid a veto while preserving parts of the bill that Congress wants.

Senate Finance Committee Chairman Lloyd Bentsen (D-Tex.) emphasized, however, that Congress -- with Democratic majorities in both houses -- is not going to cave in to White House demands. "We are not going to let them dictate all the terms of this legislation," he said. "Congress has a joint responsibility on trade, and we are going to fullfill it."

Byrd, in an interview yesterday, said he has not yet focused on the shape of the conference committee for the Senate, but he added that he expects to name Bentsen as the lead chairman. Bentsen was the main floor manager for the bill, which was passed Tuesday by a 71 to 27 majority with 19 of 46 Republicans ignoring a last-minute plea by President Reagan that they oppose the legislation.

Byrd attacked Reagan's request that GOP senators oppose the measure, saying that the 19 Republicans "were voting for their constituencies, not the White House" and were following last November's election results, which called for an end to six years of "neglect" of record trade deficits by the Reagan administration.

He dismissed charges by foreign trading partners that the bill is protectionist, asserting instead that it "goes a long way to assuring a better economic future for the American people.

"The bill will promote competition, open world markets and promote trade," he added. "It's designed to open markets and to assure access" for U.S. products.

But the reaction from overseas was quite different.

Korean Trade Minister Rha Woong-Bae, expressing concerns that the United States will use the bill as leverage to press demands that his country lower tariffs and end barriers to American products, said he hopes the "protectionist" trade legislation will be "somewhat softened" in conference, The Associated Press reported. But Rha added that it is clear that "certain U.S. import restrictions {on South Korean products} under whatever compromise will be much tougher than now."

In Brussels, the top trade official of the 12-nation European Community, Willy De Clercq, expressed "grave concern" over the bill, which he said could lead to "widespread trade disruption" by provoking the United States' trading partners to take similar actions.

Japan, a main target of the trade bill, also reacted with dismay as Hajime Tamura, minister of international trade and industry, called the legislation "clearly protectionist" and said it has "the potential to hinder the smooth flow of world trade."

Byrd, though, said he is "not surprised" that the Japanese would call the bill protectionist. "Anything that will be effective in opening export markets in Japan will be called protectionist there," he said.