The two senators heading the congressional investigation of budget director Bert Lance, possessing what they termed new material on "alleged illegalities" involving Lance, told President Carter yesterday that the budget director should resign.

The White House issued a brief, noncommittal statement of "appreciation" for this week's Senate hearings on the case, but officials said the President supported Lance's often-expressed determination to stay in his job and make a public defense of his record.

Carter said the hearings will "allow all parties the opportunity to present the facts to the opportunity to present the facts to the American people."

After a 35-minute meeting with the President at the White House, Sen. Abraham A. Tibicoff (D-Conn), the chairman of the Senate Governmental Affairs Committee, and Sen. Charles H. Percy (R-I11.), the committee's ranking Republican, said that Lance appears determined to remain in his post to defend himself at hearings scheduled to begin Wednesday.

A House Banking subcommittee will begin hearings today on the Lance affair with testimony from key officials of the comptroller of the currency's office, as well as from bank officials with whom Lance did business.

"I think it would be wiser for Bert Lance to resign," said Ribicoff, who until yesterday was considered among the strongest supporters of the embattled budget director.

The resignation calls by Ribicoff and Percy signaled the collapse of Lance's most important congressional support in his struggle to retain his job. Both senators had warmly praised the affable former Georgia banker following his confirmation hearings before their committee in January.

A White House official confirmed that Lance has told the President he wants to appear before the Senate committee and has not offered to resign. Carter "supports and respects that decision," the official said.

What was not clear was whether White House officials, faced with a new round of allegations involving Lance, have suggested to the budget director that he resign. White House officials refused to say whether they have made such suggestions to Lance.

Asked whether Lance might resign after defending himself before the Senate committee, one official said that would depend "on the nature of the allegations and Bert's ability to respond to them."

Yesterday's events, shattering the quiet of the end of the Labor Day weekend, were set in motion on Friday when White House officials were briefed by Treasury Secretary W.Michael Blumenthal and Deputy Treasury Secretary Robert Carswell on new findings concerning Lance by the comptroller of the currency.

It was clear that the briefing greatly increased White House concern over the Lance affair. Hamilton Jordan, the President's top political adviser, flew to Sea Island, Ga., where Lance was vacationing, and spent Saturday and Sunday with the budget director.

On Sunday, Lance called former Defense Secretary Clark Clifford and enlisted his help in preparing for the Senate hearings. Clifford said last night that he will meet with Ribicoff and Percy today "to learn more about these matters."

Yesterday, Lance returned to Washington and, accompanied by his wife, LaBelle, met with the President before Ribicoff and Percy arrived at the White House.

Neither senator would discuss the alleged illegalities, but Ribicoff said they were serious enough that he felt obligated to bring them to Carter's attention.

A White House official said the bulk of the new allegations grew out of a new round of investigations by the comptroller of the currency into Lance's affairs as the head of two Georgia banks. The comptroller's first report on Lance's affairs, issued Aug. 18, cleared Lance of violating banking laws or regulations, but criticized him for some banking practices and left several question unanswered.

The official said the new report deals with such items as Lance's use of bank aircraft and overdrafts on his accounts at the Calhoun, Ga., First National Bank and the National Bank of Georgia in Atlanta, both of which he headed before becoming the President's first Cabinet-level appointee.

There also was a report yesterday in the Atlanta Constitution that Senate investigators have obtained a statement from Billy Lee Campbell, a former officer at the Calhoun bank, implicating Lance in an embezzlement scheme for which Campbell is now serving an eight-year prison term.

Lance, who was president of the bank when the embezzlemnet took place, told the Constitution such allegations are "a total lie."

Percy confirmed that committee investigators recently spoke with Campbell at the federal penitentiary in Atlanta, although Ribicoff vehemently denied that Campbell has given the committee an affidavit or other written statement.

Ribicoff said the full Governmental Affairs Committee will be briefed on the latest allegations against Lance today. He said the hearings would go forward as planned.

Lance, Ribicoff said, "feels very strongly he has been maligned and wants to tell his side of the story."

In calling for Lance's resignation, both senators said they were making no judgmments of guilt but did question Lance's ability to continue as direcctor of the Officee of Management and Budget.

"I don't think Bert Lance can be an effective OMB director pending the outcome of these hearings and investigations," Ribicoff said.

Both senators also said they think further investigations into Lance's tangled financial affairs should be conducted by a special prosecutor under the terms of a recently enacted law.

The White House developments came as new charges and investigations were directed gainst Lance on at least three fronts.

Washington Post reporter John F. Berry learned that a new report from the comptroller of the currency, due to be published later this week, makes serious criticisms of Lance's recent alleged overdrafts from his bank accounts in Calhoun and Atlant and his alleged use of bank airplanes for private trips.

Berry also learned that the Securities and Exxchange Commission last week launched a full-scale investigation of possible fraud in Lance's dealings at the Calhoun First National Bank and the National Bank of Georgia in Atlanta, both of which the OMB director formerly headed.

The susbjects of the SEC investigation inccclude "insider" loans, the writeoff of some "uncollectible" loans and the use of the bank planes.

Ribicoff labeled as "a lie" the Atlanta newspaper's report that Campbell had given the investigators a signed affidavit, and Percy added that the prisoner had refused even to allow a tape recording of the interview.

The Washington Post reported last month that the Calhoun bank had been in litigation with its insurance company over the losses from Campbell'sembezzlement and had reached an out-of-court settlement for an undisclosed sum.

In the course of that litigation, the bank acknowledged that Lance became aware that Campbell "was having cash flow problems ... had actual or constructive knowledge" of the phony signatures Campbell used in his embezzlement scheme.

Whether Campbell contradicted that last assertion in his statement to the committee investigators is not known.

Campbell was convicted of embezzlement after he allegedly drained almost $1 million from the Calhoun bank, where he served under Lance.

Campbell is serving his sentence after conviction on charges involving about $125,000 of funds. According to the Atlanta Constitution story, Campbell told the investigators "Lance was in some way involved in the embezzlement."

However, Lance told aides noted that Campbell had made no such allegations at the time of this arrest, conviction or sentencing, and Perry suggested personal skepticism about the testimony of "a convicted person who obviously wants to get out."

White House officials, too, seemed less concerned about the Campbell charge than about new findings by the comptroller of the currency and the probings of committee investigators.