Douglas A. Fraser, the president of the United Auto Workers, went to the White House this week. As one of a group of business and labor representatives, he met with President Reagan to urge stronger steps against what he called ''discriminatory, unfair, and unequal trade relations'' with Japan.
A week earlier, the new president of the United Mine Workers, Richard Trumka, called on Labor Secretary Raymond Donovan in a bid for an ''open relationship'' with the Reagan administration - and for help in finding ways to put some 43,000 laid-off miners back to work.
The labor secretary also met recently with J. C. Turner, head of AFL-CIO's Operating Engineers, and this week he visited the annual meeting of the federation's 15-union Building and Construction Trades Department (BCTD) in Bal Harbour, Fla., along with Interior Secretary James G. Watt.
Secretary Donovan, invited by BCTD president Robert Georgine, spoke to the department's General Council, discussed labor's problems with leaders of union's reportedly more than 3.5 million members, and worked hard to mend ties with the group.
Ordinarily, the labor secretary's visit to construction trades meetings is routine. However, Mr. Donovan, despite his background as a construction union employer, has been out of favor with the AFL-CIO, personally and as a member of the administration.
These and other recent meetings between Donovan and labor leaders, including 14 AFL-CIO officials from Appalachian states, are not an indication that organized labor is rethinking its political opposition to the Reagan administration. There has been no change in that. It is, rather, a matter of being realistic about the need for administration support during the next two years of legislative efforts against high unemployment and other problems besetting labor.
For the White House, it is an effort to improve relations with labor by broadening contacts with individual unions, bypassing for now Lane Kirkland and others in AFL-CIO's leadership.
The administration recognizes a political need for labor - and its millions of voter-members - if it is to hold its own against Democratic gains. On the labor side, as one construction union official said in Florida, there is a growing recognition that ''we have only one President - and we need to work with him closer than we have.''
The construction industry is a good starting-point for narrowing the gap between the administration and labor. In the past, building trades unions have been more conservative than most others in AFL-CIO and more oriented politically toward Republicans. Mr. Reagan got his strongest union backing in 1980 from the ''hard hats'' in the building trades.
The administration's program for the use of revenue from a higher gasoline tax for highway and bridge construction, one that could create hundreds of thousands of building trades jobs nationally, was enthusiastically supported by construction unions.
State AFL-CIO offices from Appalachia, meanwhile, were assured by the labor secretary that funds for redevelopment of their depressed areas would not be cut from the President's 1984 budget.