Democratic National Chairman Paul G. Kirk Jr., as part of an effort to reduce the power of special-interest groups within the party, yesterday urged organized labor not to endorse a presidential candidate in 1988 before the party's nominating convention.

"In my view, the trade-union movement can strengthen the party's nominee by refraining from an early endorsement," Kirk told a meeting of the Communications Workers of America. "Let the candidates use the primary process to develop and to demonstrate their own broad political appeal and their own strong political base before giving one your full and united backing."

Kirk's recommendation was implied criticism that the AFL-CIO's endorsement of Democrat Walter F. Mondale months before the first primary or caucus of 1984 had contributed to Mondale's landslide loss to President Reagan and hurt the party's image. Mondale's Democratic opponents attempted to turn the endorsement against him, charging that he was a captive of special interests, but his advisers said the endorsement never significantly hurt him with voters and was instrumental in winning the nomination.

It was also the second time since Kirk's election as chairman that he has taken on a major Democratic Party constituency.

On the day of his election, he refused to accede to a recommendation by the Democratic National Committee Black Caucus that Mayor Richard G. Hatcher of Gary, Ind., be elected committee vice chairman. Instead, Kirk put the vice chairmanship to a vote of the full DNC, and Hatcher was defeated by Illinois Comptroller Roland Burris.

Kirk said he would take the same message to other groups, such as the National Organization for Women, which made early endorsements in the 1984 process.

Kirk said his latest proposal is "far from an offensive against labor," which strongly supported his election as chairman. He refused to criticize directly the decision to endorse Mondale and said that, whatever labor does in 1988, it should do so in a united way.

But he said he preferred to see labor "use that unity not to demonstrate the strength you possess within the Democratic Party but to help the party reclaim its rightful political heritage with the American people."

Rex Hardesty, an AFL-CIO spokesman, said yesterday, "I think the chairman's entitled to his opinion, even if it is a little premature."

AFL-CIO President Lane Kirkland, who pushed the early-endorsement policy in 1984 in an effort to reassert labor's power inside the party and help produce a presidential nominee more to its liking, said recently the chances are "very good" that labor will seriously consider doing the same thing in 1988.

Hardesty said the important thing for labor is to remain united in 1988 rather than repeating mistakes of past elections when "unions were very, very active against each other." In 1980, unions split over their support for President Jimmy Carter and Sen. Edward M. Kennedy (D-Mass.).

CWA President Glenn Watts also voiced a lukewarm reaction to Kirk's proposal.

New York Gov. Mario M. Cuomo (D), a potential 1988 presidential candidate who has enjoyed strong labor support, said yesterday that he does not care whether labor endorses early but that he supports Kirk's aggressiveness.

William Carrick, Kennedy's political director, said Kennedy "stands ready to work with Lane Kirkland and Paul Kirk" to "capture the loyalty and support of working men and women."