The Small Business Administration has begun an investigation into the nonpayment of nearly $26 million in federally backed minority business loans that have become overdue in the past 10 years.

The loans were part of an SBA program designed to strengthen minority businesses by awarding them noncompetitive business contracts.

The investigation into the loan program centers on "serious problems of mismanagement and abuse" within the SBA itself, and also focuses on possibly fraudulent acts committed by some firms participating in the program, an SBA spokesman said.

A senior White House official yesterday confirmed reports that Attorney General Griffin B. Bell and SBA Administrator A. Vernon Weaver met Wednesday with President Carter on the matter, and that Carter has approved Weaver's request for more investigators to look into the advance loan program.

"The SBA has uncovered what looks like a mess," the White House official said.

The advance loan operation is one of the smaller parts of the SBA's 8 (a) program, which began in 1968 with then-President Nixon's drive to develop "black capitalism."

Under the program, which was awarded a total of $2.9 billion worth of federal contracts since its inception, the SBA acts as the middleman in arranging for federal agencies to reserve part of their contracting work for firms owned by "socially and economically disadvantaged" persons.

Nearly $137 million in advance loans, or "payments" as they are called within the bureaucracy, have been given to minority firms since 1968. The loans are meant to be "seed money" in effect, designed to provide operating capital for minority businesses that don't have the initial funds to fulfill the noncompetitive contracts.

Last fiscal year, $36 million in advances was given under the 8 (a) program, $28.6 million of which is still outstanding, but not overdue.

The money in question, the $26 million in overdue loans that have accumulated since 1968, will be difficult to recover, said SBA spokesman Bill Combs.

"But we obviously expect to see some of this money again. That's why we started the investigation," Combs said. "What we are trying to determine is how much of it is recoverable and how much isn't," he said.

Combs said the investigation began six days ago after an SBA review board, created following House Investigations into the 8 (a) program last year, found "serious problems with the advance payments."

"The review board found that some SBA employes weren't minding the store like they were supposed to . . . They weren't following up on too many cases where people had fallen in arrears" on their loan payments, he said.

In other cases, the review board found that some 8 (a) funded businesses were using their advances to open savings accounts and draw interest. After accumulating a profit, they would withdraw the original advance and pay off the SBA, Combs said.

"Our audit people are now trying to get a handle on the size of the problem. We want to clean it up as quickly as possible," Combs said.

White House officials agree. President Carter has committed himself to increasing minority-owned businesses by 50 percent by fiscal 1980, and his main vehicle for achieving that goal is SBA's 8 (a) program.

Currently, there 1,500 companies holding about $776.5 million worth of SBA 8 (a) contracts. Only one-third of those firms now hold advance loans, according to Combs.