President Reagan has decided to summon the Republican presidential candidates to the White House for a private meeting to discourage the infighting that has recently broken out and to discuss his campaign role in 1988, White House officials said.

White House political director Frank J. Donatelli said Reagan wants to take to the road in defense of his presidency. "He has said all along he does not want to sit on the sidelines," Donatelli said. "He would obviously like to talk about his record. It's going to be an issue in the campaign, as this {Democratic} debate in Houston has told us."

Donatelli said Reagan also wants to urge the Republican contenders to abide by the "11th commandment," which Reagan has described as: "Thou shalt not speak ill of another Republican." Donatelli said a date for the meeting has not been set because of the candidates' schedules.

Reagan's decision to admonish the candidates follows a string of nasty, personal clashes involving them and their staffs. Several Republican strategists predicted that the clashes would continue despite Reagan's appeal.

"The 11th commandment is great in principle, but obviously last time we had a real contested primary, in 1976, it got violated on both sides," said consultant Edward J. Rollins, the former White House political director, recalling Reagan's challenge to President Gerald R. Ford that year for the GOP nomination.

"Everyone starts out trying not to say negative things. In the heat of battle, things will be said," Rollins said, adding that the 1988 contest would be a "tough knock-down, drag-out primary."

Already the candidates have begun turning fire on each other. Former Delaware governor Pierre S. (Pete) du Pont IV has accused the front-runner, Vice President Bush, of traveling in a "cocoon" that leaves him out of touch with average people.

The Bush camp was angered by a spate of gossip that the vice president was having an extramarital affair, which the candidate's son, George Jr., publicly denied. The rumors led to sharp words at an Iowa Republican picnic between Senate Minority Leader Robert J. Dole (R-Kan.) and George Whitgraff, Bush's Iowa coordinator.

The campaigns of Rep. Jack Kemp (R-N.Y.) and evangelist Marion G. (Pat) Robertson, who, like Bush, has not formally declared, have been troubled occasionally by imposters who telephoned news organizations and distributed false information about the time of the candidates' news conferences, according to Kemp spokesman John Buckley.

Yet another sign of the infighting occurred last week when The New Republic published an article by senior editor Fred Barnes in which a former consultant to Bush's campaign, Craig Shirley, alleged that Bush operatives were behind an anonymous mailing attacking Kemp at last February's Conservative Political Action Conference in Washington. Shirley is now in business with David Keene, a top consultant to Dole's presidential campaign.

Shirley is quoted as saying that Lee Atwater, Bush's campaign manager, was responsible for the anonymous attack on Kemp, which was attributed only to a "Conservative Truth Squad" with no list of leaders or members. Atwater denies responsibility for the mailing and refused to comment last week when questioned about it.

None of those quoted in The New Republic article denied that the anonymous mailing took place. The mailing, according to the article, described Kemp as "another two-faced sellout politician."

Bush campaign officials declined to discuss details of the article other than to deny Shirley's charges. To engage in a debate over it, said Bush political director Rich Bond, would be counter to the vice president's instructions not to criticize other Republicans. Bond said Bush has "made it abundantly clear the 11th commandment is in full force and we intend to abide by it."

A senior White House official said the idea for the White House meeting came up "when the most recent name-calling stuff started going around." The official said Reagan wants to "bring 'em all together and remind them of how Republicans ought to behave."

Reagan first expressed concern publicly about the climate of the GOP campaign in impromptu remarks to a group of political activists June 29. That was seven days after Newsweek first published an item quoting George Bush Jr. as saying that he had asked his father whether he had committed adultery and that his father denied it.

Speaking to the activists, Reagan recalled the use of the "11th commandment" when he first ran for California governor in 1966. "And, somehow, over the past years, we've begun to forget about that. And now we've got a number of candidates out there contesting with each other." He said it is up to Republicans to "make sure that all of our candidates . . . not violate that commandment."

However, GOP strategists remain skeptical that the meeting will have much effect. One who asked not to be identified said, "The truth of the matter is thus far in this contest there has been no discussion of issues. When we get to the point where there is a discussion of issues, it is going to get nasty."