In two days of nationally televised testimony, Attorney General Edwin Meese III made two major appeals to Congress and the American people. He asked them to believe that he had told "the absolute truth of what happened" and that his investigation on behalf of the president into the Iran-contra affair had uncovered all the essential facts in the case last November.

Meese told the congressional investigating committees yesterday that the administration had all relevant information possessed by Rear Adm. John M. Poindexter and Lt. Col. Oliver L. North before they were removed from their jobs and added "that not one thing that has been said since that time by Adm. Poindexter . . . has varied from what we were told that Sunday and Monday."

To accept his case, the public will have to conclude that Meese was correct in contending that no cover-up had occurred and agree with his explanation that he didn't press hard some key officials involved because they were "people I all knew to be . . . honorable and reputable individuals" -- a difficult line of defense in view of the record of deception the investigating committees have laid before the country.

Meese's congressional testimony showed how hard it may be for many in the nation and Congress to accept his account. His testimony highlighted what Sen. George J. Mitchell (D-Maine) yesterday called "the conflict of evidence on several key points" and the problem of determining Meese's credibility.

The central problem in Meese's case concerns the nature of his investigation into the unfolding Iran-contra scandal. He characterized that investigation by saying "the purpose was to resolve the conflicts and have a coherent story" -- a definition clearly open to the suggestion that it could also be construed as an attempted cover-up instead of a search for all the facts.

The greatest problem with his investigation lies in the way in which he questioned some participants and only casually talked to other key officials. Several times yesterday he drew a distinction between "interviewing" some participants and having only casual conversations with others.

This response produced the two most damaging exchanges of Meese's two days at the witness table in the Senate Caucus Room.

The first came during questioning by Mitchell about the inquiry by Meese and Justice Department aides in the days before the diversion of Iran arms sales funds to aid the Nicaraguan contras was announced and North was fired from the National Security Council staff and Poindexter resigned as national security adviser.

Meese acknowledged that in every interview he conducted with North, former national security adviser Robert C. McFarlane, Secretary of State George P. Shultz and others, a member of his staff was always present and always took extensive notes.

But when Meese spoke with Donald T. Regan, then White House chief of staff, Vice President Bush, CIA Director William J. Casey or Poindexter, that wasn't the case.

As Mitchell brought out, in a memorable refrain, in each case "you were alone with him and took no notes."

Meese explained this by saying "they were totally different types of conversations." The formal ones were where "we were seeking to elicit a great deal of information, and in which notes were important in order to record that information which we were hearing in each case for the first time." The others, he claimed, "were not for the purpose of eliciting great amounts of information. They were the casual conversations -- conversations in which I was the only person present, for example, with the president and Don Regan . . . . "

Even more telling was the questioning by Sen. Sam Nunn (D-Ga.). Nunn established that Meese never asked Poindexter directly if he had authorized the contra fund diversion; if Poindexter had told the president about it; if Poindexter believed Casey knew; if Poindexter knew whether anyone outside the U.S. government knew about it. Meese agreed with Nunn's observation that there had been "almost no direct questioning by you to Adm. Poindexter."

All of this raised many more questions than it resolved. It left many on the committees wondering how credible was the account given by the nation's chief legal officer and former prosecutor who boasted of having "gone into complex fact-finding inquiries before" and who told them, "I've spent a good portion of my life as a lawyer doing these kinds of things."