Lawyers for Marine Lt. Col. Oliver L. North yesterday notified congressional investigators that the former White House aide will refuse to answer questions in private about the Iran-contra affair.

The unexpected development led to cancellation of this morning's initial closed-door interrogation of North and may mean that he will not be questioned until mid-July when he appears at nationally televised hearings.

The chairmen and vice chairmen of the House and Senate select committees yesterday disputed the legal legitimacy of North's refusal to testify in private. But they said it left the committees with the choice of either pursuing a time-consuming contempt process against North, which could last months, or agreeing to take North's testimony for the first time at public sessions.

Last night, the Senate committee met and told its chief counsel, Arthur L. Liman, to meet with his House counterpart, John W. Nields Jr., and with North's lawyer, Brendan Sullivan, to hammer out an "ironclad agreement" that ensures North will testify in public session next month, Liman said.

Sources said that some members and staffers on the Senate panel are concerned that Sullivan is prepared to continue to raise conditions for North's testimony that will delay his appearance well beyond July.

Sen. Daniel K. Inouye (D-Hawaii), chairman of the Senate panel, said that if no agreement can be reached to guarantee North's appearance next month, he is prepared to begin contempt proceedings against North and continue the Iran-contra hearings into the fall. They are due to close in August.

The House committee will meet this morning to decide what to do about North's refusal to testify in private.

North had been subpoenaed to appear with his records today to be questioned by lawyers for the House and Senate select committees on the Iran-contra affair, under a grant of limited immunity from prosecution. But at a 7:30 a.m. meeting on Capitol Hill yesterday, Sullivan informed Nields and Liman that he believed the deposition procedure violated North's right to due process, sources said.

North's decision was supported with a legal brief arguing that any private deposition would not be covered by the immunity statute, according to House committee Chairman Lee H. Hamilton (D-Ind.). Hamilton said the brief raised questions on North's behalf about "secrecy, access to documents and double questioning."

All except one of the previous witnesses have agreed to preliminary, private sessions with committee lawyers -- a standard procedure in congressional investigations as well as in civil and criminal trials. The exception was businessman Albert A. Hakim, who was also appearing with limited immunity, and who insisted that any nonpublic testimony be given to an executive session of the committee with a required number of members present.

Earlier yesterday, Inouye said he thought it best to reject the contempt option and move ahead with public testimony by North in mid-July without the benefit of prior closed-door interviews.

But Hamilton cautioned that allowing North to have his way "could have an effect on the rest of the investigation."

Hamilton pointed out that private interviews permit committee lawyers to develop "more coherent {public} testimony" and give the attorneys a chance to verify statements given in depositions.

Hamilton also said that North's private depositions would have been useful in the questioning of North's former boss, one-time national security adviser John M. Poindexter. North also will have the benefit of having heard Rear Adm. Poindexter's testimony before giving his own.

Poindexter was interrogated in secret yesterday for the second time and is scheduled to appear as a witness beginning July 7.

Sen. Warren B. Rudman (R-N.H.), vice chairman of the Senate select panel, told reporters well before last night's committee meeting that although it is possible North might refuse to testify in public, there are strong indications that he will testify.

When North appeared before the House Foreign Affairs Committee last Dec. 9, he refused to answer questions and invoked his Fifth Amendment right against self-incrimination. At that time, however, North asserted that he was anxious to "put this issue to rest quickly and fully; and to further that end, I want to be able to provide a full exposition of the facts as I know them on this matter."

Since then, however, North has taken a number of legal steps to impede probes by Congress and independent counsel Lawrence E. Walsh. In addition to his move yesterday, which Rudman called "frivolous" but within North's legal rights, the Marine lieutenant colonel has carried on a legal battle with Walsh.

He has refused to provide Walsh's staff with a sample of his handwriting, a step that triggered a broader challenge to Walsh's authority as an independent counsel.

The committees' decision last month to grant North limited immunity was not unanimous on the House side. And some Democrats there are reluctant to make further concessions.

If the committees do not seek a contempt citation of North and he appears next month as scheduled, more extensive questioning would be required at the public session.

When the committees resume hearings next week, Inouye said, they will concentrate on filling in holes in the record of testimony in the first six weeks of hearings, and will then move on to the U.S.-Iranian arms sales.

A full witness list will be released today.

Inouye indicated that this part of the hearings will include an examination of an attempted coverup last year by senior administration officials of a U.S. role in Israeli arms deliveries to Iran. He said it would go into "how, in November 1986, officials tried to conceal possible violations of law by claiming that the November 1985 shipment of Hawk missiles was really a shipment of oil-drilling equipment."

Rudman took issue yesterday with President Reagan's criticism of the hearings. Reagan told reporters that he had "never heard so much hearsay in all my life."

"I think the president will be well-served by these hearings being completed, because he, of course, asked for them originally," Rudman said. "The president has said repeatedly that he would like to know more of what went on. And these congressional committees will find that out for him and the country."