A federal grand jury here has decided against bringing any indictments in connection with allegations that fugitive financier Robert Vesco attempted to bribe members of the Carter administration to take care of his legal problems.

Principal Assistant U.S. Attorney Carl S. Rauh said in a statement yesterday that the federal prosecutor's office agrees with the grand jury's decision and that the lengthy investigation is closed.

The prosecutor's unusual announcement of the grand jury's decision against indictments apparently was intended to put an official end to a case that had provoked intense publicity from the beginning.

The 18-month investigation opened in September 1978, after newspaper columnist Jack Anderson wrote that White House advisers Hamilton Jordan and Charles Kirbo were "linked" to a $10 million political fix to help Vesco.

There followed an extensive series of exchanges between Anderson and the White House in which each side tried to undermine the other's credibility. The Justice Department investigation itself was marred by a variety of problems, including several changes in the prosecutors' assigned to the case and public charges by the grand jury foreman of an administration cover-up.

By last summer, information leaked from the grand jury that prosecutors had doubts about the testimony of White House aide Robert M. Harden, who admitted he had been approached in February 1977 about the Vesco case by a childhood friend of his and Jordan's.

The friend, W. Spencer Lee IV, an Albany, Ga., lawyer, acknowledged that he had been paid $10,000 by Georgia businessman and convicted swindler R. L. Herring to approach the White House about Vesco's legal problems. Vesco, who reportedly is living in the Bahamas, fled the country after he was indicted in New York on charges that he looted a publicly held corporation of millions of dollars and then tried to solve his legal problems with a $200,000 contribution to the 1972 Nixon campaign.

President Carter met with Harden Feb. 15, 1977, shortly after Harden's meeting with Lee. At that time, Harden said, he told Carter that Lee had been offered "a large sum of money" to arrange a meeting between Jordan and Vesco associates. Harden said he told Carter that he had persuaded Lee to drop the plan.

At that same meeting, however, Carter wrote a cryptic note to then-Attorney General Griffin B. Bell which said, "Please see Spencer Lee from Albany when he requests an appointment." The note, which later was discovered in Justice Department files, never reached Bell.

Sources have said that the grand jury saw video-taped testimony from Carter about the meeting, but that Carter could recall few of the details of the discussion.

Suspicions about Harden's testimony were raised by prosecutors last fall after Lee -- who told essentially the same story as Harden -- failed two lie detector tests.

Harden's attorney, Robert Altman, said yesterday that he and Harden "are gratified that the investigation has confirmed that Mr. Harden is completely innocent of any wrongdoing."

Grand jury foreman Ralph E. Ulmer said yesterday that the grand jury voted against indictments in the case last week.

In August 1979, Ulmer tried to resign from the grand jury, charging that federal prosecutors had mishandled the investigation. Ulmer's accusations were vigorously denied by Assistant Attorney General Philip B. Heymann, chief of the Justice Department's Criminal Division. President Carter also strongly denied any charges that the Justice Department was trying to coverup any White House wrongdoing.

Eventually, Chief Judge William B. Bryant refused to allow Ulmer to resign from the grand jury.