On the Federal Report page Monday, Donald Stillman's post with the United Auto Workers union was incorrectly stated. He is director of governmental and international affairs.

Every Wednesday at 11 a.m., when Labor Secretary William E. Brock convenes his executive staff meeting, the conference table in Room S-2508 is surrounded by top officials whose credentials include longtime service to the Republican Party, loyalty to Ronald Reagan, and very little experience in dealing with labor unions.

With one exception.

He is a liberal Democrat and ardent unionist. His appointment so outraged conservative Republicans that it generated more than 1,000 letters of protest, including a dozen from members of congress. His heroes are union leaders whose photos cover his office walls, along with pictures of labor martyrs Joe Hill and Sacco and Vanzetti. His position on Reagan is usually a no comment.

"It gets a little awkward sometimes . . . . But I really am having a wonderful time," said Stephen I. Schlossberg, 64, a former textile union organizer and chief counsel of the United Auto Workers union. Once a top aide to the late Walter Reuther and other UAW presidents, Schlossberg now works in an administration reviled by the UAW and most unions.

"I got some letters and calls saying I had sold out" by taking a job in the Reagan administration, said Schlossberg, smiling, and shrugging off the criticism. "I got some insulting letters" from both left- and right-wing critics, he said. "But I think most people think I can be fair, and can make a contribution."

His contribution since last May is as the deputy undersecretary of labor, heading the Bureau of Labor-Management Relations and Cooperative Programs, with a staff of 69, a budget of $4.5 million, and a sometimes awkward public role to play as preacher and peacemaker.

Schlossberg is a preacher of labor-management cooperation in an era of often bitter conflict between business and unions. And he is a peacemaker as the chief liaison between the Reagan Labor Department and the AFL-CIO and other labor organizations representing nearly 20 million workers.

One of his tasks is to mend fences following the tenure of former labor secretary Raymond J. Donovan, who had hostile relations with unions. The irony, to Schlossberg's old Democrat-labor cronies, is that he may be helping Republicans solidify their hold on blue-collar votes, a concern Schlossberg does not care to discuss.

"Steve Schlossberg is doing a first-rate, superb job," Brock said at a press conference last month when asked about criticism from the National Right to Work Committee, which mounted a fund-raising and letter-writing campaign aimed at ousting Schlossberg. The committee, whose primary mission is to prohibit union contracts that require workers to join unions and pay dues, contends, in the words of chairman Reed Larson, that the appointment of a longtime union official is "totally inappropriate."

Schlossberg, a native of Roanoke, left the UAW in 1982 after nearly 20 years as lawyer, negotiator, civil rights activist, Washington lobbyist, and confidant to Reuther and his successors, Leonard Woodcock and Douglas Fraser. After several years in private law practice here, Schlossberg shocked friends and colleagues by signing on with "the enemy."

The only reason he did, he said, is that "Bill Brock is a wonderful human being, and a supersensitive and caring man" who asked Schlossberg to do a job both men strongly believe in. "My attachment [to the administration] is with Brock . . . . If he went to the World Bank, I would get the hell out of here," Schlossberg said, referring to a recent offer Brock declined.

Schlossberg's position provides him a pulpit from which to spread the gospel of workplace cooperation as a key to meeting foreign competition. He crisscrosses the country speaking to big business, big labor, academia and anyone else who will listen to the message that American free enterprise will be in big trouble if executives, middle managers and workers can't work together to improve productivity.

In dozens of speeches, conferences, and department-sponsored research projects, Schlossberg -- and Brock -- stress that nonadversarial labor relations and even power-sharing between workers and owners can be profitable to all.

The bureau has some favorite examples that it highlights at conferences: the General Motors Co.-UAW plan to try labor-management cooperation at the futuristic Saturn auto plant to be built in Tennessee; Xerox Corp.'s relationship with its union, the Amalgamated Clothing and Textile Workers, and American Telephone & Telegraph's with the Communications Workers of America. These companies share some information and power with unions. In exchange for more job security, workers agree to scrap rigid work rules and job classifications that management detests.

"One reason I am excited about more flexibility over work rules is that we can make jobs more interesting, make workers more involved in the process of work," Schlossberg said. He sees such trends as helping to "humanize" work.

"Auto workers organized a union, not over money, but over having some control over their destiny, over the inexorable tyranny of the assembly line, the machines, and the supervisors," he said.

The values espoused by Reuther and other labor leaders appealed to Schlossberg, he said, partly because he grew up as a Jew in Depression-era Virginia and was exposed to anti-Semitism, racism and failures of social justice.

After graduating from the University of Virginia, Schlossberg worked in his uncle's department store and became vice president of the Roanoke Chamber of Commerce. He also became politically active in fighting the conservative Byrd machine in Virginia. "I was sort of a Yuppie, I suppose, and I thought I could have an activist life on the side, dealing with social justice. But you can't."

So he decided to leave the business world in 1949 to recruit in the southern mills for the International Ladies Garment Workers Union. As a southerner, "I was one of the few labor organizers who didn't speak with a New York accent . . . . I spoke to workers in their language, I was quite successful," he said. But the job had a few drawbacks: "I had been beaten up, roughed up and arrested . . . living in lousy motels, and earning $65 a week."

He gave it up and, at age 36, became a lawyer. His gregarious down-home manner and legal skills came in handy, said Donald Stillman, UAW legislative director: "I have seen him during the big auto bargaining sessions, when people were tense. He would get everybody laughing at a series of great jokes, and 10 minutes later, he'd have helped work out a very knotty legal problem."

Schlossberg's role is different now, but the problems remain knotty. He says, "I don't believe in the tooth fairy. I don't believe we have all the answers to becoming competitive by labor-management cooperation. But it's a tremendous part of becoming competitive -- to motivate people better, and increase the quality of work, and tailor machines to people, instead of people to machines.