Jack Anderson's columns claiming that President Carter has approved an invasion of Iran presented newspaper editors across the country this weekend with the dilemma of how to publish news that, if true, would be one of the most damning revelations about any president in history.

For most editors, the handling of the first Anderson column, which was released for Monday publication, seemed to hinge on two major issues -- Anderson's credibility and the editors' reluctance, regardless of their editorial judgments, to be seen as suppressing information they knew was being broadcast on radio and television.

Many editors appear to have published the first column routinely despite its sensational content. Others went out of their way to highlight or denounce the columns, which were mailed late last week to Anderson's roughly 970 daily newspaper subscribers.

The Montrose Daily Press in Montrose, Colo., recognized the sensational nature of Anderson's allegation that a president would plan an invasion with his eye on abetting his reelection campaign.

Managing editor Richard Day put the column on the paper's front page with an editor's note explaining: "We feel that the allegations contained in the following column are the most serious ever made against any president of the United States . . ."

The note said "Anderson enjoys high credibility among journalists," and Day added that "we have no reason to believe that Anderson is making it up."

At the Fayetteville Observer in North Carolina, editorial page editor John Eslinger was equally struck by the gravity of the allegation, but was less impressed by Anderson's reputation and the substance of the column.

Eslinger called the Anderson charge "worse than accusing the president of murder. If Anderson is right, Eslinger wrote in his Monday paper, the president has committed an impeachable offense. If he is wrong, Eslinger wrote, Anderson should be drummed out of journalism.

The problem facing the editors was how to tell whether Anderson is right or wrong.

The Washington Post, Newsday and the New York Daily News tried to verify the Anderson charge. They failed to find verification, and did not print Monday's column.

Thomas Giordano, managing editor of the Evening Herald in Sanford, Fla., felt strongly that Anderson's five columns on the invasion were irresponsible, he said. However, he decided to publish them because he has no Washington bureau to check out the assertions.

It would be worse not to run the columns and then learn some other newspaper had turned up confirmation of them than to run them "offset by an editorial," Giordano said.

"We didn't want to get accused of suppressing anything," said Jim Hampton, who runs the editorial page of the Miami Herald. The Herald did not publish the first Anderson column yesterday, but reconsidered its decision in part because of telephone calls from readers who had heard about Anderson's claim. The Herald will run the first Anderson column today.

Anderson scoffed at papers that did not run the column. "I thought newspapers were supposed to publish information, not suppress it," he said yesterday.

"I would consider any newspaper that suppressed a story because its own reporters could not confirm it to be arrogant," the Associated Press quoted him as saying.

David Hendin, vice president and editorial director of United Feature Syndicate, which distributes Anderson's columns, said that he got several telephone calls from editors worried that the embargo, preventing publication of the first column until Monday, would be violated but none expressing concern about the column's allegation.

The Modesto Bee in California broke the embargo over the weekend, and several papers, including the Chicago Sun-Times, then published articles citing Anderson's charge and the White House's immediate denial.

Ralph Otwell, editor of the Sun-Times, said, "We handled it as responsibly as we could. Ignoring it would be foolish since it was all over radio and TV."

"Yes, I did ask Jack about the columns," Hendin said. "We largely depend on the long-time reputation and credibility of Jack Anderson as an investigative reporter."