The Senate investigation of Billy Carter hurried toward an uncertain conclusion yesterday as members of the special subcommittee in charge of the inquiry decided there was no need for President Carter's testimony.

Subcommittee Chairman Birch Bayh (D-Ind.) said the panel agreed at an executive session that there were no areas that demanded either an "eyeball-to-eyeball" meeting with the president or even a sworn statement from him in response to written questions.

Instead, Bayh said, the subcommittee will hand White House lawyers a rundown of what information it still needs and let them compile whatever answers the president or anyone else at the White House can supply.

Facing an Oct. 4 deadline for a report to Congress, the senators also decided yesterday to make it just an "interim" report, but with little expectation that there will be any need for another. The record will be kept open, however, in the event of some unforeseen development.

"The report will be as complete as we can make it at this time," the subcommittee's chief counsel, Philip Tone, told reporters. "We're going to treat it as if it were our last report."

The investigation of Billy Carter's dealings with the Libyan government and the Carter administration's awareness of those activities has thus far produced more evidence of what one senator has described as bumbling and incompetence than of any real impropriety.

Bayh said yesterday that what remains to be done consists primarily of "drawing loose ends together" and clearing up contradictions in some of the testimony.

As part of that effort, several of the subcommittee's lawyers spent the day taking a new deposition from Billy Carter at the offices of his Washington lawyers.

Looking relaxed the president's brother emerged in later afternoon to tell reporters that much of the questioning was devoted to telphone conversations he made on key dates.

When President Carter met with Libya's chief diplomat in the Oval Office Dec. 6, for example, Billy Carter was busy on the phone through the day, calling the Libyan Embassy and the Charter Oil Co., a Florida-based corporation for which he was seeking an increased allocation of Libyan oil.

Billy Carter called the sequence pure "happenstance" and said it was "ridiculous" to think the calls might have been intended to give the Libyans the impression that he had a hand in the White House meeting. He said he was not even aware of it until the president publicly disclosed it this summer after Billy registered as a foreign agent.

The president's brother said the December phone calls merely reflected a continuing effort on his part to swing the Charter oil deal, independently of what was going on in Washington.

In other developments yesterday:

Subcommittee officials refused to comment on the Atlanta Constitution's disclosure that civil rights leader Jesse Jackson was named as another potential Libyan oil broker in the same intelligence report that CIA Director Stansfield Turner brought to White House attention March 31.

Jackson denied being a Libyan agent, but told the newspaper he had written the Libyan Embassy in Washington on behalf of the Wallace Co. of Tuskegee, Ala., a black-owned oil company. He also told The Washington Post several weeks ago that the chief Libyan diplomat here, Ali Houderi, had made a $10,000 contribution to Jackson's Operation PUSH in Chicago at its annual fund-raising event Dec. 18.

The subcommittee made public a santized version of Turner's testimony Sept. 9 when the CIA director defended his decision to alert the White House to Billy Carter's Libyan oil project. Turner declined to say whether he thought it proper for White House National security adviser Abigniew Brzezinski to have, in turn, warned Billy Carter against the project, but he said he saw no reason why Brzezinski could not have done so without jeopardizing the source of the intelligence information.