Federal Reserve Board Chairman Paul A. Volcker yesterday firmly rejected a proposal that some part of the Third World's debt be canceled because the borrowing nations are overburdened with the interest obligations on their debt.

"That kind of approach is a dead end," Volcker said at a conference here on the future of the World Bank. He asserted that all of the borrowers "have a large stake in servicing the debt," and that it "is demonstrable, with rare exceptions, that the debt can be serviced."

He cited, as an example, Brazil, which he said has continued to register economic growth and improvements in its balance of external accounts while making regular interest payments.

"I simply think the case for maintaining continuity in debt service is overwhelming," Volcker said. "All of the borrowers have a very large stake in servicing their debt in an orderly way if they want to participate in the world economy and continue to grow."

But Mexican Undersecretary of Finance Francisco Suarez-Davila told the conference that "some external relief has to come" to his country from Japan and other major nations whose international surpluses have been swollen "by a windfall from the drop in the price of oil."

Suarez-Davila said that Mexico faces a recession, with a decline in economic activity of almost 5 percent, yet is faced with a $600 million monthly debt-servicing charge. "This process cannot continue. We require cooperation from creditors," he said.

He warned that "there is no more room" for cuts in Mexico's public expenditures, and, in effect, appealed to the World Bank and the governments supplying funds to slow down their demands for emphasis on the private sector and market-oriented activity.

"This may be workable, but the sense of reform has to come from within," he said.

Volcker and Suarez-Davila addressed separate sessions of a conference sponsored by the Overseas Development Council and attended by World Bank President-designate Barber Conable and other bank and administration officials.

In the course of the two-day session, many of the principal speakers urged, as did Suarez-Davila, that Japan contribute more to Third World development. But Volcker, in adding his endorsement to the idea, warned that it would be difficult to accomplish. "Japan has this enormous surplus, and they like it," Volcker said.

Volcker, lining up with the Reagan administration, also came out against a general capital increase (GCI) for the World Bank now, arguing that the institution "has enough capacity and liquidity for the immediate future to carry out both project- and policy-lending on any scale that is practical."

Without any new funds, Volcker said, the bank can achieve "a sizable increase in its disbursements." Treasury Secretary James A. Baker III has repeatedly said the same thing, in almost the same words, in rejecting proposals for a GCI of up to $100 billion in new callable capital, or funds committed but contributed as needed.

The Fed chairman's comments on debt relief came in answers to questions on speeches made by other conference participants at the opening session on Monday night.

Former West German chancellor Helmut Schmidt had said that the Third World debt "will never be paid back," and that the loans to the poorest among them should be written off. Another speaker Monday, New York banker Felix Rohatyn, called for a restructuring of the debt by conversion of short-term debt into long-term debt -- up to 30 years, with substantial reductions in the high interest rates originally charged.

Volcker, who had turned down a possible appointment to succeed retiring bank President A. W. (Tom) Clausen, said that he took a "conservative" approach on the many proposals that had been made for reforming the bank and for stretching its resources.

For example, he indicated he was against the frequently made proposal that the bank's "gearing ratio" -- the dollar-for-dollar limit on the bank's loans in relation to its capital -- be increased.

But he said that in meeting the current debt crisis, the bank would have to "blend some new approaches" with its traditional operations along three lines:

As the bank is thrust more into financing structural economic reforms in the developing countries, its work will increasingly overlap that of the International Monetary Fund.

More of the bank's lending over the next few years must be for "policy" purposes, as distinguished from projects -- but the two have to be complementary.

The bank "is going to have to work more closely with other lenders and investors, public and private" around the world.

Volcker said that since the bank has had mostly harmonious relationships with client countries, without some of the hostility that has been shown to the IMF, "that gives it a head start" in urging economic reforms in the borrowing countries.

An essential lesson to be learned from the IMF experience, he said, "is that before the bank can make policy loans, it needs to have knowledge of political support in the borrowing countries . . . .

"It's important that changes not be imposed from the outside, and that the bank programs have support at home," Volcker said. He added that he sees a helpful change in attitude among many of the borrowing nations that "have a new respect for liberal, open economic orders."