President Reagan would like better relations with organized labor. Lane Kirkland, AFL-CIO president, would like better relations with Mr. Reagan. In a conference at the White House they discussed their stormy relationship. They found big philosophic differences remained between them.
Reagan told a labor delegation invited to the White House, led by Mr. Kirkland, that he would not be ''estranged'' from unionists and wanted closer contacts. He would ask the vice-president and the secretary of labor to arrange regular meetings with a broad spectrum of labor leaders. He asked labor support on foreign affairs and defense despite differences on domestic affairs.
Kirkland and fellow leaders indicated they wanted a bigger olive branch. Referring to a tentative proposal to modify the administration boycott of air traffic controllers Kenneth Blaylock, president of the American Federation of Government Employees commented, ''I don't think that's enough.'' But the labor movement is in weakened position for bargaining.
Unlike other industrial countries, four out of five American workers are outside trade unions, whose 15 million membership has been shrinking as a proportion of the total population. Reagan is seeking to curtail or abolish some of the social agencies that Kirkland prizes most. Inflation is putting a squeeze on union wage negotiations with employers. And every day, it seems, newspapers carry an ominous list of layoffs in many of the biggest firms.
With the exception of the tightly controlled Teamsters Union, members of most trade unions voted against Reagan in 1980 or didn't bother to vote.
More recently, the antagonism has manifested itself in several ways:
* Unlike most recent presidents, Reagan was not invited to the annual AFL-CIO convention.
* A spectacular outdoor solidarity rally here Sept. 19 assembled a quarter million people. Organized by Kirkland, it attacked the Reagan administration.
* The President fired 11,500 union air traffic controllers after an illegal strike Aug. 3 and until recently has been adamant about not compromising with the controllers.
Labor spokesmen argue that sacrifices asked by the administration to balance the budget are imposing unfair burdens on middle- and lower-income working groups to the advantage those in upper-income brackets.
One big exception to labor hostility to the Reagan administration is the 300, 000-member International Brotherhood of Teamsters, which is the largest union in the nation.
Reagan met with Teamsetr President Roy Lee Williams and the 21-man Teamster executive board Dec. 1, prior to his meeting with the hostile Kirkland group. Teamsters and their employers, the trucking companies, oppose the recent deregulation of the trucking industry and urge Reagan to reverse it.
At the Teamsters meeting, Reagan hinted that he is considering lifting a three-year ban on government service for the ousted air traffic controllers. This is part of an administration effort to cool labor's anger with the President, anger that is said to have prompted his meeting with Kirkland.
The rift between the President and union leaders is deeper than at any time in recent years. Today, labor is more closely aligned with the Democrats than it was under the late AFL-CIO president George Meany. Few think Reagan can close the breach. But he can moderate the view of some that he is a deliberately union-busting President.