President Carter sought to patch up his strained relations with organized labor last night with a huge Labor Day picnic on the White House lawn and a personal tribute to its ailing leader, AFL-CIO President George Meany.

Glossing over the differences that have kept them at verbal sword's points, Carter thanked the labor leaders for their support on his energy program and the strategic arms limitation treaty, and appealed for a reconciliation of differences on national health insurance.

But many presidents of major unions were notable by their absence, and the applause for Carter, while polite, indicated he has a long way to go in whipping up labor's enthusiasm for his reelection.

Speaking of Meany and other union leaders, Carter said they have always been "in the forefront when there was a dynamic struggle" and been a "stabilizing and inspirational factor for all the presidents."

He told the crowd of nearly 900 -- several hundred fewer than had been expected to attend -- that Meany had just called to express regrets that a "virus attack" prevented him from being at the picnic.

"He's a fine man," said Carter of the 85-year-old labor chieftain with whom he has had difficult and sometimes acerbic relations. "He was kind of reading me my report card on the telephone [Meany once gave him a C minus]. He said if I wouldn't tell what was on it he wouldn't tell either."

Without touching on the recurrent expectations that Meany, sidelined by hip and other ailments for most of the year, will step down this fall, he said there are "three things a president has on his mind . . . national security, always present; the Congress, always present, and President Meany, that's the third one." He completed his speech by asking for a round of applause for Meany.

In shelving his prepared text in favor of off-the-cuff remarks, Carter passed over what could have been the greatest applause-getter of the evening -- an assertion that "we cannot conquer inflation by sacrificing the jobs of working Americans" and a pledge that labor will be "at the table during every economic decision we make."

A presidential aid said that Carter stood by the remarks in the text and attributed this omission to the fact that Carter, like Meany, was running a fever from a virus.

Differences over economic policy, including anti-inflation wage guidelines, have been one of the biggest irritants in relations between Carter and labor, which helped elect him in 1976 and is only reluctantly and partially moving into his reelection camp for 1980.

Significantly, aside from the Meany tribute, Carter got the most applause from the gathering for his comments on national health insurance, where labor has aligned itself closer to the program advanced by Sen. Edward M. Kennedy (D-Mass.) than to Carter's proposals. Most union leaders agree that Kennedy has more support among labor than Carter, and some who are moving toward Carter say they are doing so only because Kennedy has not indicated he will run.

Although the presidents of some of the biggest unions did not attend, almost all major ones, including two of the largest independents, the Teamsters and the United Auto Workers, were represented by some of their Washington officials. Only one, the International Association of Machinists, headed by Carter arch-critic William Winpisinger, had indicated beforehand it would boycott the party. Meany's heir-apparent, AFL-CIO Secretary-Treasurer Lane Kirkland, attended and was praised by Carter for his advice during energy consultations this summer.