Attorney General Benjamin R. Civiletti told Justice Department officials who had just made a breakthrough in the Billy Carter investigation last June to "wait 10 days or so" to "see what happens," thhe lawyer in charge of the case said yesterday.

During that interval, Civiletti spoke to President Carter privately about the investigation and assured him that "there would be no punishment" for Billy Carter if he would register as a foreign agent.

The Justice Department said Civiletti would have no comment until he testifies before the special Senate subcommittee investigating the controversy. He is scheduled to appear today.

Justice Department lawyers who appeared at yesterday's session also disclosed that the president's national security affairs adviser, Zbigniew Brzezinski, is under investigation for possible violation of the espionage laws and for unauthorized disclosure of classified information.

The inquiry involving Brzezinski stems from his having called Billy Carter last March, hours after receiving a highly sensitive intelligence report about Billy's efforts to win an increased allocation of Libyan oil for a U.S. oil company. Brzezinski has said he called the president's brother to warn him that the deal could be exploited politically by the Libyans and create "considerable embarrassment for this country."

Assistant Attorney General Philip B. Heymann said the Justice Department's Office of Professional Responsibility is attempting to determine whether there was "any compromise of classified information" on Brzezinski's part.

The new episode involving the attorney general's conduct, revealed in testimony from Joel S. Lisker, head of The Justice Department's foreign agents registration unit, drew a quick demand for his resignation yesterday afternoon from Republican presidential candidate Ronald Reagan's camp.

At a news conference yesterday afternoon, Reagan campaign director William Casey called on Carter to request Civiletti's resignation in light of what Casey described as a 1976 Carter campaign pledge to fire any Cabinet member who lied.

This summer, Civiletti at first denied ever speaking with the president about his brother's case but them acknowledge that he had done so last June 17 after a White House meeting on judicial appointments.

Lisker told the Senate subcommittee yesterday that he and one of his superiors, Mark Richard, briefed the attorney general June 11 about admissions Billy Carter had just made to them about $220,000 in payments from the Libyan government.

"The attorney general said, 'Well, let's wait 10 days or so,'" Lisker recalled. He said the attorney general made the remark "in the context of [suggesting] maybe he'll register -- let's see what happens.'"

Civiletti has told Senate lawyers who have interviewed him that he does not recall making the remark, according to sources familiar with the investigation. r

At the time of the June 11 briefing, however, the attorney general apparently was aware that he would be seeing the president June 17. Sources said Civiletti had made the appointment on the morning of June 11, a few hours before Lisker and Richard arrived to tell him of their interview with Billy.

The prolonged questioning at yesterday's Senate hearing -- the first public session devoted to the Justice Department's handling of the 18-month Billy Carter investigation -- also brought out that:

When Billy Carter showed up in Washington June 11 for meetings at the Justice Department and the White House, the FBI was assigned to tail the president's brother around town because officials suspected he might have made the trip primarily to receive a cash payoff from the Libyans.

Civiletti withheld two top-secret intelligence reports about Billy Carter's dealings with the Libyans from everyone else at the Justice Department from mid-April until early June -- although Brzezinski already had called Billy Carter to discuss the contnts of one of the reports.

Subcommittee chairman Birch Bayh (D-Ind) suggested that favoritism was involved. "We know that the very day Dr. Brzezinski read the report he received in March, he picked up the phone and spoke to Billy Carter about it," Bayh pointed out. Yet, the senator added, the attorney general "withheld from key personnel in the criminal division, who have the clearance to receive the most sensitive information, the very information that Dr. Brzezinski related immediately to the target of the investigation."

At one point, Heymann indicated that he felt Civiletti had gone too far in withholding the reports he had gotten in mid-April. All the attorney general told him then, Heymann testified, was not to close the case because of top-secret information Civiletti had acquired.

Heymann said he didn't ask Civiletti what the information was, although safely made "some of it available in the form of leads" to be pursued by Justice Department investigators. One of the reports indicated that the Libyans might be on the verge of making a transfer of money to Billy Carter. lThe other dealt with the efforts of the president's brother to obtain an increased allocation of Libyan crude oil for an oil company that stood ready to pay him a multimillion-dollar commission.

The attorney general did not provide subordinates with any of these reports until June 4, when Heymann told Civiletti that Lisker had come across information about the Libyan payments to Billy from Lisker's own "separate, highly sensitive intelligence sources."

Asked why Civiletti felt he could tell his aides in June what he wouldn't tell them in April, Heymann said the attorney gneral knew by June 4 "that we were developing the same information from our sources. I suspect he felt, wrongly, that ours were less sensitive."

In any case, the subcommittee was told, the investigation had moved into high gear, prompting double checks of old leads, including a report from Billy that he had once spoken with White House appointments secretary Phil Wise about the status of some C130 military air transports purchased by the Libyans. Wise had been questioned about this on March 14 by an FBI agent, but a fresh interview was needed because "the agent misunderstood the time frame" of the reported phone call.

Lisker, however, said that Wise wouldn't talk to the FBI again until Lisker called the White House aide around June 4 and warned that "he might have to talk to a grand jury" if he wouldn't make himself available to the FBI. Wise, the subcommittee was told, made himself "immediately available."

Five days later, on June 9, Lisker was called by Americus, Ga., attorney John Parks, who asked about the status of the investigation and "whether it was going to a grand jury." Lisker said he refused to discuss the matter because Parks said he was not acting as Billy's lawyer but was "just calling as a friend."

The next day, Billy called. Lisker said he told the president's brother that "I know a lot more than I did" earlier and that "we need to talk."

Carter came to Washington the next day. Heymann authorized his physical surveillance by the FBI. At the interview, the president's brother at first insisted he had gotten nothing from the Libyans but gold bracelets, a saddle and some expense-paid trips, but Lisker said the Justice department knew better.

"He squirmed a bit in his seat and said, Well, I got a $200,000 loan. I asked for $500,000 and I got $200,000.'"

Lisker said he then asked whether there as "anything else" and Billy owned up to a $20,000 payment, describing that at the time as partial reimbursement for $40,000 in expenses he had run up on behalf of the Libyans during a 1979 visit to Georgia by various officials of the Arab regime.

Carter left after about an hour for an appointment with Brzezinski at the White House. Lisker said he "tried to put him in an FBI taxicab" that was waiting downstairs, but Billy insisted on taking another.

Because "it was my job to finger Billy" for the FBI, Lisker said he escorted the president's brother to the street "and the FBI picked him up at that point." (In a subsequent report, FBI officials said they did not observe the president's barother "in contact with any Libyan officials" that day.)

Lisker and Richard now had Billy Carter's own admissions, instead of intelligence reports that felt they couldn't use. The two men said they soon found themselves in Civiletti's office with the attorney general and his top deputy, Charles Renfrew, telling them about the $200,000 in payments.

"We also told Mr. Civiletti about the [FBI] surveillance," Lisker recalled. "He seemed surprised. 'Annoyed' might be a better term. He didn't see any reason for it."

Lisker said they also expressed their concern about Brzeninski's having told Billy he was aware of the proposed oil company deal. Billy had mentioned this during the interview and Lisker said he "saw a potential violation of the espionage law" on Brzezinski's part in disclosing intelligence information of the most sensitive nature.

Civiletti, however, "said we shouldn't jump to conclusions" and suggested that Brzezinski may have learned of the proposed oil deal from some other source. Finally, Lisker said, the attorney general suggested the 10-day wait.

Lisker said he took the attorney general to mean simply that no criminal indictment or civil suit should be filed in that time. Lisker said he was "very relieved" to hear that, because he wasn't prepared to act in 10 days anyway.

Heymann told the subcommittee that sometime in June, before Civeletti's June chat with the president, the attorney general told him:

"Phil, I shouldn't tell the president anything about the Billy Carter investigation. Do you agree?'"

Heymann said he did agree. But he said t hat he sees nothing wrong in Civilett's having then gone to the White House and telling the president what he did. He said he feels the attorney general was realy thinking of "investigative information" that he did not intend to discuss with the president.

"When he talked with the president on the 17th," Heymann reasoned, "he's really not talking about investigative information."

Subcommittee Chairman Bayh suggested that the attorney general, in his June 11 chat with the president, may have committed the Justice Department not to prosecute the president's brother without the knowledge of the Justice Department lawyers in charge of the investigation.

According to the president's own notes of he brief June 17 conversation with Civiletti, "He [Civiletti] told me that Billy ought to acknowledge if he was an agent" and that "there would be no punishment for him."

Lisker and Heymann insisted that they were still actively considering criminal prosectuion until June 27, when they decided on a civil lawsuit instead.

Heymann said Civiletti's assurance to President Carter that there would be no prosecution of Billy if he registered, was in any case, "legally incourrect." Lisker, in turn assured the subcommittee that no one at the White House or the Justice Department ever conveyed such an idea to him or tried to influence his decision in any way.