The top officials of the International Monetary Fund and World Bank issued an unusual joint statement yesterday calling on commercial banks to act quickly to implement Treasury Secretary James A. Baker III's plan to increase lending to Third World debtor nations.

The statement by IMF Managing Director Jacques de Larosiere and World Bank President A.W. Clausen was intended to reassure some foreign banks reluctant to participate in Baker's call for an additional $20 billion in commercial bank loans to the Third World over the next three years.

The push to step up commercial lending was part of a three-pronged world-debt strategy outlined by Baker at the IMF and World Bank annual meeting in Seoul in October. His plan also would boost multilateral development banks' loans by $9 billion over the next three years, and insists on economic reforms by borrowing nations to encourage a greater commitment by the private sector.

Baker argued that the debt-ridden developing countries must have additional foreign funds to resume economic growth, both to reduce social pressures and to make it easier to cope with their heavy debt payments.

Latin American nations alone have $350 billion in foreign debts, two-thirds of it owed to commercial banks.

Reagan administration sources said yesterday that they believe the banks are close to reaching agreement to participate in the Baker initiative. But bankers said there are issues to be resolved, such as the role that creditor governments such as the United States will play in the program.

U.S. bankers said they are worried, for example, that bank regulators will make it difficult for them to increase their exposure in the Third World. They also worry that some governments might reduce trade assistance they give to debtor countries at the same time commercial lenders are boosting their loans.

The commercial banks have held three international meetings and numerous national and regional conferences on the Baker plan.

And the Latin American governments -- the major target of the new Baker strategy -- themselves will convene a conference of their foreign and finance ministers in Uruguay Dec. 16-18 to try to draft a cohesive response.

Sentiment among American banks has been divided between those that support the Baker plan as the only way of insuring their current Third World investments, and those who feel that unless international institutions guarantee their loans, the Baker proposal is tantamount to throwing good money after bad.

European and Japanese banks have been even less enthusiastic, pointing out that U.S. banks are the primary lenders to Latin America. Said one source involved in preparation of yesterday's statement: "We sensed a feeling among the foreign bankers that it was not necessarily appropriate for them to fall in line with a strategy devised by the United States government alone."

Representatives of European banks said they would be more comfortable responding to a concern expressed on an international level, the source said. "The international banks said they needed a clear signal as to where the IMF and bank stand on the Baker plan , so we decided to give them a signal -- and to do it jointly."

The joint statement declared: "The IMF and World Bank, in close collaboration, are ready and willing to play their parts in the implementation of the Baker initiative and to that end will cooperate fully and constructively with their membership and with all parties in these concerted efforts to deal with debt problems and establish the basis for sustained economic growth."

It noted that Baker had called for "a program for sustained growth," supported by the two institutions, that would require the borrowing countries to adopt comprehensive economic policies that would enable them to pay their foreign interest payments, reduce inflation, and resume healthy growth and trade, while reducing inflation, so that they can pay their foreign debts and still grow.

Officials would not directly confirm reports in Europe that the United States had been seeking a commitment from European banks by Sunday. But one official at the IMF said that "de Larosiere . . . expects a positive reaction" from these banks now that the joint statement has been issued. And Treasury sources confirmed they had told the banks they hope there will be something "substantive" by the middle of this month.