A "real recovery" from the Third World debt crisis is under way and is likely to continue, a leading private expert said yesterday.

In a highly optimistic evaluation, William R. Cline Jr. of the International Institute of Economics said that world economic growth has been the main factor in turning things around from a "disastrous" performance in the first few years of the 1980s, outweighing negative factors such as continued high interest rates.

But he conceded at a press conference that political strains in the debtor countries remain strong, because the effects of the recession are still evident and there is great opposition to high interest rates, which took a new upward turn earlier this year. The internal problems of inflation control are proving to be more intractable than reducing the external debt, he added.

Although Cline's view is largely endorsed by the International Monetary Fund and the U.S. government, a World Bank agency said yesterday that the situation of private industry in the developing world is still "precarious," with even efficient firms fighting for survival because real borrowing costs run between 30 and 40 percent.

Cline's overall evaluation is that the system has weathered the storm, and that, even at the depths of the crisis, "We didn't see a political collapse." He cited in particular economic recoveries in Mexico and Brazil.

The success in managing the debt problem proves that "radical" programs such as debt forgiveness would not have been wise, Cline said. "It remains appropriate to manage the problem as one of illiquidity, not insolvency, and on a case-by-case basis."

He reported that the 19 largest debtor nations had succeeded in cutting their external deficit from $56 billion in 1982 to $23 billion in 1983, and he predicted further improvement over the next several years. His assumptions include a 3 percent real global growth rate from 1983 to 1987, oil prices holding at $29 a barrel, a U.S. prime interest rate of 13.5 percent, and a 20 percent decline in the dollar exchange rate over the next two years.

Cline's analysis was contained in a new book, "International Debt: Systemic Risk and Policy Response," an updated version of an earlier study published by the institute.

The World Bank's cautionary note was sounded by the International Finance Corp., its affiliate dealing with the private sector in the Third World. In its annual report, the IFC said that the debt crisis had triggered many business bankruptcies in the poor countries.

According to the report, it was politically easier in many poor countries to restrict credit than to fight inflation by cutting government spending and social programs. The real burden of monetary restraint therefore fell on private companies, not on subsidized public sectors, the report said.

According to the IFC, although the debt crisis has waned, it is far from clear that others can duplicate the "shorter-term success" such as that achieved by Mexico. It cites an IMF projection that debt-service ratios for the 25 major debtor countries as a group will show no improvement through 1990.

Despite upbeat assessments, the IFC report noted that, in many of the 37 countries in which it operates, "Private industry is still fragile and not yet strongly established." It cites widespread bankruptcies, as well as forced mergers causing undue concentration of industry.

With strong support from the United States, the IFC is embarking on a five-year program to boost the flow of private capital into Third World countries.

The IFC said that it is seeking to achieve a 6-to-1 ratio of investment from private sources to IFC's own expanded outlays over the next five years. In June, the IFC announced its intention to double its capital and undertake $7.4 billion worth of investments in projects valued at $30 billion in that period.

Its report shows the dollar volume that it committed fell to $696 million in 1983 from $846 million in 1982 because the prolonged recession discouraged private investment.

One of IFC's major interests in the years ahead will be to encourage independent oil companies to expand activities in developing countries. The United States has been unhappy with World Bank efforts to finance government energy projects, and is anxious to see the IFC make a major effort in the private sector instead.

The IFC said it plans to put up about $100 million in equity investments in 23 oil and gas exploration projects that would cost a total of about $1 billion.

Nonetheless, the World Bank management and principal shareholders, including the United States, have been impatient with the IFC's scorecard, and Executive Vice President Hans A. Wuttke, a West German national, is resigning as of Oct. 1. He will be replaced by Sir William Ryrie, a British national.