A large number of the world's rich nations yesterday reaffirmed the need "in principle" for a strong International Development Association, the soft-loan lending agency of the World Bank, according to a spokesman.

At the conclusion of a two-day meeting of the IDA deputy ministers precipitated by a shortfall in the American contribution, a bank spokesman said that the institution was "very satisfied" with the determination of other contributing nations to try to make up the U.S. deficit.

The IDA lends money without interest (but at a small service charge) for a 50-year term. It is the largest such source of subsidized aid to the poorest nations.

The Reagan administration cut the U.S. contribution from $1.1 billion to $700 million this year. Under IDA rules, that normally would trigger pro rata reductions by other contributors, slicing the total fiscal 1982 IDA lending program from $4.1 billion to $2.6 billion.

But several countries agreed yesterday to put in their full shares regardless of the U.S. cut, narrowing the gap by about $500 million. Of this total, $120 million will come from Great Britain as a result of an earlier-announced Whitehall decision.

Other full-share contributors will be Austria, Belgium, Greece, Italy, Luxembourg, Saudi Arabia, Kuwait, Australia, the Netherlands, the United Arab Emirates, and Japan. The deputies of some of these countries said that the commitment would have to be confirmed formally by their governments, a bank official reported.

Several other countries--including Canada, West Germany, and France--did not agree to go above a level of contributions proportional to the U.S. share, but promised to see that the balance of their original commitment to the IDA would "go to the poorest of the poor countries." One possibility that was discussed is a "special fund" outside of the regular IDA pool, for which procurement would be tied to the lending or borrowing countries.