President Carter, beginning to position himself for a three-way campaign in the fall, will not participate in any debates with independent presidential candidate John B. Anderson, White House press secretary Jody Powell said yesterday.

Powell said that Carter, who has avoided opportunities to debate his Democrat rival, Sen. Edward M. Kennedy (D-Mass.), has decided to refuse joint appearances with Anderson because "once you start opening up the system, it is hard to say where you draw the line."

"It is not our intention to participate in debates with third, fourth or fifth party candidates," the spokesman added.

Informed of the White House statement in Houston, Anderson yesterday recalled Carter's refusal to debate Kennedy and said, "I suppose I should not be surprised, and yet I am.

"For the president, who has had chief responsibility for foreign and domestic policy for the last 3 1/2 years, to decline to participate in a debate with an independent candidate, I think that shows contempt on his part for the political process."

The president's decision appeared to be the beginning of a White House strategy to isolate Anderson, portraying him as little more than a fringe candidate with no chance of winning in November. But while Anderson, whose candidacy Carter aides fear will damage the president more than that of Ronald Reagan in the fall, was the target of the debate decision its impact will fall first on the League of Women Voters.

The league sponsored the nationally televised presidential debates in 1976 and plans to do the same this year. However, with Carter now threatening to boycott a debate involving Anderson, the league will clearly be under pressure to exclude the Illinois congressman or risk scuttling its highly visible debate project.

In that event, other organizations undoubtedly would be willing to sponsor head-to-head debate between Carter and Reagan, in which the president has said he would participate. "I would think there will be ample opportunity to debate the Republican candidate," Powell said in reference to this likelihood.

Betsy Gutman, a league official, said formal debate invitations have not been sent to any candidates, but will be to the eventual Democratic and Republican nominees. She said the question of inviting third-party candidates and other issues are to be studied during the summer by an advisory committee headed by Newton Minor, the former Federal Communications Commission chairman, and Anne Armstrong, a former ambassador to Britain.

The decision on whether to invite Anderson to participate in the debates will be made by the league's board of trustees by the end of the summer, Gutman said.

Reagan, campaigning in Pasadena, Calif., was asked about Carter's refusal to debate Anderson. The former California governor said that he would be willing to debate either Carter or Anderson in any combination and pointed out that the president had "been reluctant to debate within his own party."

Reagan had said previously that he would be willing to debate with Anderson.

"I saw no reason why, if John is a legitimate candidate in a kind of three party movement, that if there is a debate why he shouldn't be included," Reagan said. He then reiterated his own willingness to debate Carter one on one and was asked why he thought the president wouldn't debate Anderson.

"Maybe because he thinks they might be trying to appeal to the same voters," Reagan replied.

Carter strategists are anxious for the president to debate Reagan, believing that the former California governor, who has already run into criticism for mixing up his facts, will come off poorly before a national audience, although he did well in several GOP debates this year. However, they are clearly just as anxious to avoid doing anything that would add credibility to Anderson's campaign, which they see as a threat to undercut Carter in key states, possibly throwing them to Reagan.

Adopting this attitude, Powell yesterday spoke derisively of Anderson's candidacy, calling it a "fantasy" to believe he could be elected.

"For the most part, the assumption has been that people are interested in a debate between the two major-party candidates," Powell said. "It is generally accepted that the next president will be one of those two men and I don't think anyone seriously disputes that."

Asked if he could foresee a set of circumstances that might lead to Anderson's election, Powell relied, "No."

The debate decision was only the latest example of White House fears that Anderson could damage the president in the fall. In recent weeks, Carter aides have been among those encouraging publicity about Anderson's three attempts in the 1960s to have a reference to belief in Jesus Christ incorporated into the Constitution.

The Democratic National Committee is also exploring the possibility of filing legal challenges to Anderson's attempts to get on state ballots as an independent candidate in November.

In 1976, former Minnesota senator Eugen McCarthy and former Georgia governor Lester Maddox, both then independent presidential candidates, unsuccessfully sought a court order that would have forced the League of Women Voters to include them in the presidential debates of that year.