President Carter's controversial plan to withdraw U.S. ground forces from South Korea passed a test yesterday when the House International Relations Committee approved the transfer of $800 million worth of arms and equipment to Korea.

The proposed pullout has run into such heavy opposition in Congress that Carter on April 21 was forced to order a slowdown in the first phase of the withdrawal.

Chairman Clement J. Zablocki (D-Wis.) said yesterday's action "responds to President Carter's request for action by Congress now so the administration can proceed with the withdrawal while strengthening South Korea's ability to deter an attack."

But the committee's approval of the equipment transfer is only one of the endorsements the president's plan needs before it can be put into effect.

In order to compensate South Korea for the pullout of 32,000 U.S. troops, the administration wants to turn over to the Koreans the $800 million worth of equipment now in the hands of the American forces stationed there and give South Korea an additional $275 million in arms credits. Both actions require congressional approval.

However, congressional leaders have warned that the aid proposals are in jeopardy because of the Korean influnce-buying investigation and the basic opposition of many lawmakers to the pullout program.

That opposition was underscored last week when the House Armed Services Committee issued a report charging that the withdrawal would contribute to instability in Asia. The same committee also approved an amendment that, if passed by the full Congress, would require Carter to leave at least 26,000 ground combat troops in Korea until a peace agreement is achieved between North and South Korea.

The uncertainties created by this opposition forced Carter to slow down his original plans for a first-phase withdrawal of 6,000 troops by the end of this year. Instead, the number to be withdrawn this fall will total 3,400 combat and support troops, with the remainder to be left in Korea until next year.

Despite the slowdown, the administration says it still plans to pull out all U.S. ground forces by the end of 1982. But before it can proceed with even the first phase, it needs Congress' backing for the compensatory support promised to the South Koreans, and yesterday's action by the International Relations Committee marked a step in that direction.

The committee's approval, in the form of an amendment to the fiscal 1979 military assistance bill, was passed by voice vote after Zablocki established informally that a majority of the members favored giving Carter authority for the transfer, which is scheduled to take place over a 4-to-5 year period.

But the committee tacked on two restrictions proposed by Rep. Stephen J. Solarz (D-NY). One set an $800 million limit on the value of the transferrde equipment, and the other specified that no equipment can be transferred until the U.S. troops leave Korea.