President Carter reaffirmed his faith in budget director Bert Lance yesterday, asserting in the face of skeptical press questioning that no one has shown Lance to be guilty of anything "illegal or even unethical."

At a news conference, the President was questioned at length about Lance, whose free-wheeling style as the head of two Georgia banks before he joined the government has produced the Carter administration's first embarrassing brush with allegations of potential conflict of interest.

"I have spent a great deal of time trying to become acquainted with the charges or allegations against Bert Lance," Carter said. "It means a lot to him. It means a lot to me personally as a friend of his. It means a lot to me as President, responsible for the integrity and reputation not only of my Cabinet officers but myself.

"I don't know of any allegation that has been made or proven that Bert Lance did anything illegal or even unethical."

In the course of making his defense, the President volunteered that he and his wife at times have overdrawn their bank accounts - a practice for which Lance, as a bank officer, was critized by the office of the comptroller of the currency.

He also suggested that the Lance investigation may result in stricter banking laws and regulations dealing with some of the practices in which Lance engaged.

Throughout the news conference, Carter made several references to the comptsroller's report, saying he had studied it closely because of the importance of the questions. But in response to questions, the President revealed an unfamiliarity with the details of the report.

Carter seemed surprised when one questioner asked about the competence of a federal budget director who, even after assuming his government post, had seven overdrafts on his personal account.

"I didn't know - you are referring to Mr. Lance?" the President said.

Told such a finding was in the comptroller's report, he replied, "I see. Well, obviously it is better not to write overdrafts."

It was at this point that Carter acknowledged having overdrawn his own account, "not deliberately but because of an error or because of higher priorities that were assigned to other responsibilities that I had at the time." He also said that he did not think the overdrafts reflected on Lance's ability to manage the federal budget.

"I think that there is no doubt that Bert Lance is one of the more competent and intelligent people that I have ever known in my life," he said.

The comptroller's report shows that on seven occasions between Jan. 15 and June 7, 1977, Lance's account at the Calhoun National Bank in Georgia was overdrawn. The amounts involved ranged from $32 to $3,745.

On a related topic, the President was questioned about the propriety of overdrafts on a campaign account Lance maintained at the Calhoun bank when he was running unsuccessfully for governor of Georgia in 1974.

Carter replied that Lance maintained other accounts at the bank as well as certificate of deposit of more than $100,000 and that these more than compensated for any overdrafts on the campaign account.

However, the details of the comptroller's report differ with that contention.

The report shows that Lance maintained a $110,000 certificate of deposit at the bank during this period. But on numerous occasions during 1974, according to the report, overdrafts on the campaign account exceeded $110,000, rtaching a high of $152,706 between Nov. 22 and Dec. 5, 1974.

At this same time, the report showed, Lance's personal account at the bank and the account of his wife, LaBelle, frequently were overdrawn, by as much as $110,493 in the case of Mrs. Lance.

A spokesman of Lance said after the news conference that the budget director in 1974 had pledged all of his assets to the bank to cover any possible overdraft problems withe the campaign account. But according to the comptroller's report, the pledge consisted of an undated form in which Lance promised to pay any liabilities to the bank.

Carter acknowledged that, should further investigation or congressional hearings come up with new information about Lance, or any other administration official, he would have to reasses his position.

But on the whole, the President's defense of his old friend and choice to head the Office of Management and Budget was as storng as it was last week, when he introduced Lance at a news conference following release of the comptroller's official.

"But," he added, "I also think it is part of our process that if allegations are unfounded or if there is no illegal or unethical conduct revealed, that the accused public official should be exonerated. And this is the way I assess, after great study, the Bert Lance case."

The President also said that he does not believe the Lance affair has given rise even to the appearance of a conflict of interest in the administration.

He said he knows of now alternative to the way the administrative has handled problem, which essentially has been to require high officials to put their private assets into so-called "blind trusts" over which they had no control.

"You can't expect a public official to dispose of all their net worth before they come to government," he said.

The President began the news conference by making three announcements dealing with foreign policy, a somewhat unusal practice for him which cut into the time available for questions. The only questions he was asked dealing with domestic matters concerned the Lance affair.