The board of regents of the Smithsonian Institution reported yesterday that it has divested the bulk of its holdings in companies that have business operations in South Africa.

Since May, when the regents voted for divestment, the institution has sold $26 million in stocks in 39 companies. Now the Smithsonian has partial holdings of "a little over $1 million," according to the regents, in three companies -- E.I. du Pont de Nemours and Co., Ford Motor Co. and ITT Corp. A spokeswoman for the Smithsonian said the institution is moving ahead "with all practical speed" to complete the action.

Yesterday's regents meeting adjourned after a little over two hours so the 17-member board could attend the public opening of its two new museums, the Arthur M. Sackler Gallery and the National Museum of African Art.

In other business, the regents discussed the status of the Museum of the American Indian but did not take any new action. In May the regents decided to look into acquiring the collection. Yesterday, there was, according to the Smithsonian spokeswoman, "general agreement that it is an issue that bears watching and it will be an issue a long time sorting itself out."

There are two bills in the U.S. Senate addressing the future of the collection, much of which is housed in a warehouse in New York. Sen. Daniel Inouye (D-Hawaii) introduced a bill last week that urges the building of a new museum on the Mall that would house the prestigious collection. In May Sen. Daniel Patrick Moynihan (D-N.Y.) introduced a bill that would keep the collection in New York at the historic Custom House and not make it part of the Smithsonian.

The Smithsonian has never had any direct investments in South African companies, but its $214 million investment portfolio as of last April included approximately $27 million invested in companies that had operations in South Africa and were signatories of the so-called Sullivan Principles. The institution has been moving steadily toward total divestment since 1985, when the regents voted to sell holdings in companies that had not adhered to the Sullivan code. Established by the Rev. Leon Sullivan, the principles established guidelines for U.S. corporations to follow in South Africa in the areas of salary and living conditions.

The $26 million has been reinvested in other stocks, according to the Smithsonian. The endowment is used for activities and purchases not covered by its federal appropriations. The total fiscal year 1987 budget for the Smithsonian is $273.4 million.