The FBI has begun an internal investigation of whether its officials, including James B. Adams, the new No. 2 man, deliberately hid from congressional investigators the extent of the bureau's allegedly illegal break-ins.

The new "administrative inquiry" was delegated to the FBI by Attorney General Griffin B. Bell when he announced the indictment of FBI former acting director L. Patrick Gray III and two high-ranking aides 10 days ago. The men were charged with approving break-ins against friends and relatives of members of the early 1970s.

The FBI's office of professional responsibility will conduct the inquiry, with the goal of determining "the causes of the FBI's failure to discover and report all instances of surreptitious entry," according to Bell.

That unfinished Part of the Justice Department investigation was given little notice at the time the indictments were announced.

But FBI and Justice officials consider the new inquiry important because of Adam's potential involvement and because the integrity and credibility of FBI officials.

Adams said yesterday in an interview at his office that he did have a role in approving erroneous material forwarded to Congress during the 1975 investigations by the House and Senate intelligence committees and the General Accounting Office.

"It's fair to ask the question of who, if anyone, knew the information was incomplete," Adams said. "I can and will tell you that I didn't know" the information was wrong.

Adams, who was named associate director just three weeks ago, said he will have no role in reviewing the work of the new inquiry because the internal FBI investigators will report directly to FBI Director William H. Webster. "I do expect to be interviewed," he said.

FBI officials told the congressional investigators that they had uncovered no evidence that the so-called "black-bag" jobs continued after 1966, when FBI then-director J. Edgar Hoover ordered that breaks-ins against domestic targets be stopped.

In July 1975, then FBI director Clarence M. Kelley told reporters the same thing.

In the spring of 1976, however, the FBI found records which showed that agents from the New York field office were still conducting break-ins in 1972 and 1973.

That discovery triggered what became a criminal investigation by a team of Justice Department civil rights attorneys under the direction of Assistant General J. Stanley Pottinger.

It also led Kelley to announce that he had been deceived by unknown subordinates.

Pottinger, now a Washington attorney, said in a telephone interview that he told members of the Senate committee in late May that they had been misinformed by the FBI the year before. He then incorporated the possible cover-up investigation into the larger inquiry, he said.

That summer, Richard Fogel, who directed the GAO study of the FBI domestic intelligence investigations, learned that in one instance, at least, he too had received bad information.

That GAO audit - first involving FBI investigative files - depended on bureau summaries of sample cases, Fogel said in a telephone interview. "I was contacted by one of Pottinger's group who said there were indications they (FBI officials) had covered up the fact of break-ins in one sample," he said.

The GAO investigator testified about the matter before a New York grand jury in December 1976, he said.

Sources familiar with the investigation said that this part of the cover-up investigation led to a recommendation that James Ingram, then head of intelligence for the FBI's New York office, be charged with making false statements to federal investigators.

Ingram, now deputy assistant director in charge of domestic security and terrorism investigations at FBI headquarters, refused to answer questions about whether others higher in the FBI chain of command approved or were informed of the incomplete report to the GAO, sources said.

Ingram case, but said: "I have tried to impress on everyone that the credibility of the bureau depends on how accurately we respond to these types of inquiries.

"We can live with what mistakes we've made in the past. We cannot play games and decided which facts to make available," he said.

The potential FBI cover-up investigation apparently was not a high priority item either for pottinger's original task force or an expanded Justice Department team that took over last December, when the first team quit after a dispute with Bell.

Bell's referral of the incomplete investigation back to the FBI for administrative, rather than criminal, inquiry is indicative of his effort to get the painful problem of the FBI break-ins behind him.

"It's a question," Adams said, "of whether you pursue everything right down to the last item, or do you let us [in the FBI] pursue white collar and organized crime."