The non-Communist world's financial leaders concluded a two-day meeting here yesterday with a general agreement that economic growth in the industrial world will have to speed up in order to cut high unemployment and to help the development of poor nations.

A communique issued at the conclusion of the International Monetary Fund's Interim Committee session said there were many "unsatisfactory" economic developments in the world over the past year. It cited especially "a drift toward protectionism," which it attributed to low economic growth rates and high unemployment.

It spelled out a "medium term" strategy for the next two years under which each country is supposed to take measures best suited to itself for non-inflationary growth and the reduction in either trade surpluses or deficits.

Unless this strategy is followed, British Chancellor of the Exchequer Denis Healey said, "There is a risk of being trapped in a deflationary spiral" - in other words, a worldwide recession.

In private meetings among the key leader, however, at least a few nations - notably West Germany - resisted presistent pressures from the United States, Britain and others to boost their economic targets. The atmosphere, nevertheless appeared to be cordial and free of the tension that had marked discussions of this problem in the past.

U.S. Treasury Secretary W. Michael Blumenthal said at a press conference that he was pleased with progress made for two reasons.

First, he said it was "understood and appreciated" that the United States is giving full attention to its problems concerning energy, inflation and economic growth.

Second, Blumenthal said that a clear understanding had arisen in the past two days that if the problems of growth and inflation all over the world are not settled, "tendencies toward protectionism would be intensified."

Healey, who is also chairman of the Interim Committee, said in summarizing the discussion of the world's economic outlook, that poor countries were correct to be concerned about protectionism, and to be skeptical about the industrial world's commitment to faster growth.

The growth issue, which proved a dominant theme, was also discussed yesterday morning at a breakfast session among the so-called Big Five finance ministers - those from the United States, West Germany, Japan, Great Britain and France.

It was learned that both Blumenthal and Healey urged the West German government to consider measures to boost the economic growth rate beyond the 3.5 percent level projected by Bonn for this year. But private German forecasters say the growth rate this year is not expected to top last year's 2.5 percent.

Specifically, sources said, the West Germans were urged to consider lowering taxes as a stimulus, but the Germans firmly resisted all such pressures, saying they would observe economic conditions in the late spring before making any new decisions.

In a conversation with reporters later, West German Finance Minister Hans Mattoefer said that "we will not be pushed." Mattoefer, who accompanied Blumenthal back to Washington last night, said that the "Big Five" meeting was extremely useful for clarifying positions.

"We want growth, too," Mattoefer said. "We have elections coming up in 1980. But 2.5 percent growth is not exactly despicable." He nevertheless left the door open to an adjustment in the West German government's policy before the economic summit scheduled July 16 and 17.

The Interim Committee communique said that there were some favorable developments in the world economy last year, including a reduction in the surpluses of the oil exporting countries.

It listed on the other side of the ledger "the slow and uneven pace of recovery" from the 1974-75 recession, historically high levels of unemployment, slow growth of world trade, continuation of high inflation, and "the maldistribution of current account balances, and instability of exchange rates among the industrial countries."

The committee said it paid special attention to the problems of developing countries, recognizing their vulnerability to recession in the industrial world and to reduced access to the industrial countries' markets.

But the committee, as expected, failed to take any specific action on several issues high on the list of the poor nations' demands. There was no decision made on a new allocation of Special Drawing Rights (SDRs) - a specially created asset distributed proportionately to the 134 IMF members. But the United States, in principle, is understood to have accepted a future token issue of SDRs, perhaps at a rate of about $2.5 billion to $4.5 billion a year. Healey said "a significant majority" of IMF members favor a new allocation of SDRs.

There was also no decision taken on new quotas - the amount paid in the IMF by member countries - to supplement the existing $48 billion resources of the organization. These issues, however, including a proposal of the United States to relate the SDR allocations to future quotas, will be taken up at the September annual meeting of the IMF.

According to Healey, there is practically a consensus that quotas should be increased about 50 percent.

In his first meeting with international financial leaders, Federal Reserve chairman G. William Miller was said to have been "very impressive" in outlining U.S. determination to control inflation and excessive monetary growth.

The session completed one formality, the designation to French treasury head Jacques de Larosiere as managing director of the IMF, to succeed H. J. Witteveen. Witteveen will complete five years service, and Larosiere will take over on Sept. 1.