Secretary of State George P. Shultz opened a new administration effort to win congressional approval of the president's Caribbean Basin initiative yesterday, calling the assorted proposals vital for poor countries striving to avoid deepening economic crises.

In his first such mission to Congress since becoming secretary, Shultz asked the Senate Finance Committee to give its part of the embattled aid plan "priority attention" and not be distracted by the controversial elements which have left it unsupported so far this year.

He called the package of direct aid, investment incentives and trade preferences essential to help Caribbean countries avoid economic instability, which leaves them prey to "violent minorities on both sides of the poitical spectrum."

His joint appearance with Treasury Secretary Donald T. Regan underscored the administration's determination to keep the plan alive despite several defeats in both houses this year.

The foreign aid part of the plan was rejected on a point of order last week in the House, which did not debate a $350 million aid appropriation because no authorization bill had been passed. That was when the administration decided to make a renewed effort for all parts of the initiative in the presumably friendlier Senate and hope for later concurrence by the House.

The initial reception yesterday was optimistic, with Senate Finance Committee Chairman Robert J. Dole (R-Kan.) promising another hearing and a final markup soon on the tax and trade elements of the proposal which fall within his panel's jurisdiction. But the Senate path is strewn with the same obstacles that wrecked the Caribbean plan in the House. The AFL-CIO opposed the trade and investment segments yesterday, claiming they would cost Americans jobs as industry moved plants and other investments to the Latin countries.

Several industries, including leather goods, also oppose the trade preferences, arguing that they would enable foreign competitors to move exports through the Caribbean countries with a small amount of work performed there. Industry lobbying in the House succeeded in exempting several products from the trade preferences.

Also, the Senate Foreign Relations Committee has voted to transform the direct economic aid sections into a World Bank program, much to the administration's displeasure.

Proponents have tentatively agreed to an administration plan to win quick approval of the investment and trade elements and move them to the floor where the World Bank section could be overturned and the entire package sent on to the House.

Skepticism about how strongly the administration wants the plan surfaced yesterday. Sen. John H. Chafee (R-R.I.) endorsed it but said many sympathetic supporters doubt the depth of the administration's commitment. Assistant Secretary of State Thomas O. Enders assured him that it has "top legislative priority" in the administration.

A key provision would extend duty-free privileges to a number of products, except textiles and clothing, and require that only 25 percent of the work on those products be done in the Caribbean countries. That is lower than the 35 percent usuallly required and has led to the charge that countries such as Japan, Taiwan and South Korea could win large shares of U.S. markets by passing their products through the Caribbean countries.

An AFL-CIO lobbyist, Stephen Koplan, charged that under that provision "massive trade diversions . . . can be funneled through any one or any combination of 28 Caribbean countries by satisfying a ridiculously low local content requirement of 25 percent . . . ."

Shultz met that argument by claiming that the competition generated would be minor. "The imports that would be affected by our trade proposal are at present less than one-half of 1 percent of our total imports," he said. There would be no "serious negative impact" as a result of the proposed changes, he added.