In his first 10 days on the job, Labor Secretary William E. Brock has spent as much time with most top AFL-CIO officials as his predecessor, Raymond J. Donovan, spent in four years.

Moving swiftly to melt the Reagan administration's icy relations with most of organized labor, Brock has courted union support, named a former United Auto Workers official to a top job and told the AFL-CIO executive council that he wants labor to play an active role in helping shape policy.

Brock's overtures have been cordially but somewhat skeptically received by unions. AFL-CIO President Lane Kirkland said after a 90-minute meeting with Brock Tuesday that President Reagan's policies "do not give us great grounds for optimism . . . . The tone and basic philosophy and ideology and objectives of an administration are set by the White House, and the White House hasn't changed."

Brock, in an interview yesterday, said his initiatives toward labor are part of his belief that unions "fulfill an enormously important role" and that labor-management cooperation is crucial to America's ability to compete with foreign countries.

Brock, a former Republican National Committee chairman, also said he believes that his effort to "restore" the Labor Department to an active role could greatly help the GOP by showing its commitment to youth, minorities, women, the unemployed and to overall economic growth.

"What I would like to try to demonstrate is . . . that the Republican Party really does care about the people of this country, about the opportunity of all to have a chance to have a decent job, work in a safe and healthy environment, have an adequate pension plan. A party that puts its emphasis on growth," Brock said.

Brock, who is widely credited with rebuilding the GOP during his 1977-80 term as RNC chairman, said he believes that "if we meet our commitments" by creating jobs and serving constituencies such as youth, women and minorities, Republicans could emerge as the nation's new majority party.

"No party has a monopoly on trying to care about, or work with, or communicate with blue-collar America," he said. "Both parties have a responsibility to do it as effectively as they can."

Brock, who served eight years in the House and six in the Senate, had an AFL-CIO "approval" rating of 14 percent on labor-related votes. He said yesterday that he does not expect to agree with unions on many issues but that he would present their viewpoint effectively in the Cabinet.

Brock said he shares Kirkland's "eloquent point," made during their meeting Tuesday, that the administration must distinguish between "expenditures and investments," because many social programs are investments in the future, in such areas as job training.

"I will be an advocate of programs that attempt to address the difficulties of minorities, young people, unemployed people, of people that need training . . . ," Brock said, adding, "I think it is my responsibility to be sure that, as we pursue those goals, we do so in the most cost-effective possible way."

But Brock said he would not answer questions about agencies such as the widely criticized Occupational Safety and Health Administration until he has had more time to review the issues. Nor would he comment on Donovan's policies and performance.

Brock, who served as U.S. trade representative from 1981 until last month, said the nation "cannot afford to have labor and management going at each other all the time as enemies or adversaries . . . . We have to compete in the world and we are not going to compete if we are fighting each other."

"We cannot compete on the basis of wages," Brock said, referring to the considerably lower wage base of developing countries. Instead, he said, "progressive" employers and unions must reduce costs and boost their competitive position by mutually solving problems that hinder productivity.

"The progressive labor unions know very well that they have to help management deal with problems like absenteeism, lower productivity, low pride and an unhealthy workplace," he said.

Brock said his hiring of former UAW official Stephen Schlossberg as deputy undersecretary for labor-management relations is intended to promote development of cooperative programs.

Brock, whose family operates a nonunion candy manufacturing firm in Tennessee, said he would not be averse to joining a union. "I certainly could see myself in a union situation. If I were in an industry that required representation, I could be a very active member," he said.