Senate Majority Leader Robert J. Dole (R-Kan.) yesterday said that Congress probably will vote on some type of protectionist legislation by Oct. 15, putting still more pressure on the Reagan administration to formulate a new trade policy acceptable to Capitol Hill.

Dole, visiting Taiwan, Hong Kong and South Korea, as well as Japan, has warned government leaders in those countries that Congress is serious about compelling them to open their markets to U.S. goods.

"The message we leave in each place is that we don't have much time," Dole said. "As soon as Congress reconvenes in September -- I would say within 30 days of that date, say between Sept. 15 and Oct. 15 -- there will be a vote on some kind of protectionist legislation. We don't call it protectionist. They do. We call it fairness legislation."

Dole spoke from Hong Kong on the "Today" show on NBC.

Dole did not say what piece of import-restricting legislation might be passed first. Several key members of Congress have complained that no legislation would be necessary if the administration had an effective trade policy.

The administration's policy of opposing protectionist bills "may accurately reflect policy, but they are not reflecting the politics of this issue," Dole said. "I believe trade will be one of the big issues in 1986 and 1988" elections. "And that's the message we've given every leader of every country we've visited."

Both Democrats and Republicans have been trying to take the lead in the trade issue, with prominent members of both sides sponsoring legislation to restrict imports.

Meanwhile, the administration said it is reviewing its current policy of opposing protectionist legislation and the possibility of exchanging it for a tougher stance against trading partners. President Reagan is expected to announce a new trade policy in the next few weeks.

As proof of the lack of a policy, members of Congress cite last year's record U.S. merchandise trade deficit of $123.3 billion, which is expected to grow to $150 billion this year. However, many economists say that the trade problem is caused primarily by the high value of the U.S. dollar -- which makes domestic goods more expensive relative to imports -- rather than the absence of a tough trade policy.

"We've indicated the mood of the Congress, the mood of the American people," Dole said. "Rightly or wrongly, the American people perceive . . . unfair trade practices causing a lot of our problems."

"The bottom line is we have a $140 billion trade deficit," Dole continued. "A $50 billion trade deficit with Japan, $11 billion with Taiwan, about $5 billion each with Hong Kong and Korea." If solutions to the trade problem cannot be reached between trading partners, "we have to do it through the legislative process," Dole said.

Dole was asked whether the fact that the executive branch maintains a free trade stance while Congress is more protectionist sends mixed signals to U.S trading partners.

"I would hope the administration would understand that Congress really has the primary responsibility for trade legislation," Dole said. "It's in the Constitution. Now we've ceded much of that authority to the administration, to the executive branch, over the past 10 to 15 years and I think Congress is now ready to reclaim that authority."