Many Third World debtor nations are now moving into a second stage of the international debt crisis in which the role of the World Bank "is likely to be much more critical" and the role of the International Monetary Fund diminished, Federal Reserve Board Chairman Paul A. Volcker told a House Banking subcommittee yesterday.

Volcker said that, in the new phase, looking beyond the immediate firefighter's role played by the IMF, the focus should be on the need to sustain growth at a time of shrinking availability of private credit.

"In that context, the role of the World Bank and regional development lending institutions is likely to become much more critical. The need for innovative approaches and even closer cooperation with the fund seems to be evident," he said.

Volcker said that while the bank's major focus on financing large projects is likely to continue, "it also is quite possible that as a matter of relative priority," such projects "with returns deferred far into the future, could give way to areas where more effective use of the existing capital stock is emphasized, with quicker and more evident returns."

But he came down against some of the more exotic remedies for the Third World debt problem, such as governments taking over and writing off existing debt to private lenders. Volcker recently criticized his vice chairman, Preston Martin, for proposing solutions to the debt problem that he said encouraged a belief there "can be easy answers to difficult problems."

In his testimony before the subcommittee on international development institutions and finance, chaired by Rep. Stan Lundine (D-N.Y.), Volcker also called for continued U.S. support of the IMF and multilateral development banks, "including, as and when the need is demonstrated, financial backing in the form of capital increases."

Expansion of the World Bank's role in the debt crisis is gaining support and is expected to be a major topic of discussion at the bank's annual joint meeting with the IMF in Seoul in October. The Reagan administration has also urged the bank to accept a greater role in development but so far has not committed itself to a capital increase for the bank as proposed by President A. W. Clausen.

Volcker's prescription for the proper bank and IMF roles in the second stage was given only in general terms. But he cited recent joint efforts in Colombia as a possible clue to the future. In Colombia, the bank is a major lender for specific projects and "structural adjustment loans," a relatively new bank technique for quick disbursement of money that has an impact on short-term, balance-of-payments needs.

Although Colombia hasn't had to go to the IMF for emergency needs, it keeps the IMF informed. As announced last week, the IMF has agreed to monitor the economic progress Colombia is making.

Volcker said that all of the big debtor nations, in Latin America and elsewhere, need to move "from a situation of endemic financial crisis to another stage in development, looking toward what is necessary to sustain growth. As they do so, the particular skills and resources of the World Bank become increasingly relevant. Heavy reliance on the shorter-term tools of the IMF should then be phased down and out."

Lundine said he scheduled the hearings to examine the question of how the bank and IMF relationships should be adjusted to provide the best stimulus to long-term Third World growth.