The House approved President Reagan's Caribbean Basin Initiative yesterday after turning back strong protectionist objections by organized labor.

Democratic and Republican leaders joined to deny labor charges that thousands of American jobs will be lost as a result of the program. It will provide duty-free access to U.S. markets for $800 million to $1 billion worth of Caribbean exports, based on 1981 trade figures.

Backers of the bill said this was just a drop in the bucket of duty-free imports into this country and that it was the least the United States could do to encourage democratic stability in the region.

The crucial vote came Wednesday night on a motion to adopt a closed rule insulating the bill from a series of amendments sought by the AFL-CIO and a long list of individual unions, from the United Steelworkers to the Stone, Glass and Clay Coordinating Committee.

The rule, which kept Reps. Richard A. Gephardt (D-Mo.) and James L. Oberstar (D-Minn.) from offering the restrictions, was approved, 212 to 204.

The measure was given final approval yesterday afternoon after assurances from Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) that his panel would maintain "alert and effective surveillance" to make sure the program has no adverse impact on the domestic job market.

"There is much too much at stake," House Majority Leader James C. Wright Jr. (D-Tex.) said in urging passage. "We are not going to win Latin America by guns alone . . . . These are the friends most vital to our future. And friendship is a two-way street."

The bill authorizes Reagan to set up a free-trade area for unlimited duty-free entry of various articles from a potential 28 nations and territories in the Caribbean Basin. Those that have communist governments or fail to meet other conditions in the bill will not be eligible without special waivers.

Two-thirds of Caribbean exports, not counting petroleum, already enter the United States duty-free, but according to the Ways and Means Committee much potential trade is still restricted.

To qualify for duty-free treatment under the bill approved yesterday, articles must be imported directly from a beneficiary country, must be substantially fashioned in the Caribbean and must be of at least 35 percent "local content" from one or more of the designated countries.

Oberstar protested in debate Wednesday night that the 35-percent requirement was too loose and that so-called "import-sensitive" products such as steel, watches, glass and electronic components should be added to the bill's list of ineligible items.

He also maintained that the bill should have included U.S.-style safeguards for worker health and safety to prevent continued exploitation of workers in the Caribbean countries.

Proponents said labor's fears were grossly exaggerated and that the changes it wanted would simply emasculate the program.

Rep. Sam M. Gibbons (D-Fla.) said he was convinced the program would create more American jobs by creating fresh markets for U.S. tools and equipment. He said he also feared disaster if tariff laws were opened to amendment on the House floor.

Despite the leadership efforts, 174 House Democrats voted to defeat the rule and open the bill to amendments. The Republicans provided the clout that kept the rule intact.

The House then gave final approval to the measure yesterday afternoon, 289 to 129, with a provision calling for annual assessments from the Labor Department of the impact on U.S. labor. The bill now goes to a House-Senate conference.