MIAMI BEACH, OCT. 26 -- AFL-CIO President Lane Kirkland vowed today that organized labor would prove in the next presidential election that it has not lost its political clout.

Kirkland, in the opening address to the federation's 17th biennial convention, said, "For those who have spurned our petitions for the redress of grievances, claiming that we have lost our clout, perhaps we can be more convincing this time around."

He said that the Senate is now under Democratic control thanks in large part to the efforts of organized labor in the last election.

But Kirkland, stung by the charge in the 1984 presidential election that labor was simply another special interest, went to great lengths today to show that labor's legislative agenda was the agenda of a broad coalition of working people -- union and nonunion.

"As we go into another presidential election year we shall be exposed, I expect, to the mindless abuse of the term 'special interests' -- just as we, along with our allies in that effort, were when we called upon the Senate to block President Reagan's latest effort to tilt the scales of justice on the Supreme Court for privilege and against people for years to come," Kirkland said.

Labor and its allies in Congress are supporting a package of bills they hope to make synonymous with family issues rather than union issues. These bills include an increase in the federal minimum wage, parental leave for both the father and the mother when a child is born, child care benefits and mandatory health insurance benefits.

Sen. Edward M. Kennedy (D-Mass.) underscored the emphasis on the family when he addressed the convention later in the day. After listing the same legislative issues that Kirkland spelled out, Kennedy said: "Democrats have the issues to run on in 1988 -- and to win on. I am convinced that the people are ready to respond."

Although organized labor believes it has the issues to win next year's presidential election, it is still searching for an acceptable candidate.

The AFL-CIO earlier postponed a meeting of its general board because no candidate even came close to winning majority approval from the federation's members. Until a consensus emerges, the leadership has urged its member unions not to endorse anyone.

Kirkland used his opening address to explain his position on the reaffiliation of the 1.8 million-member Teamsters union, three decades after the union was expelled for corruption.

"The reaffiliation of the Teamsters, after 30 years outside our house, is another major step toward the goal we have always sought and to which I pledged my best effort eight years ago -- the reunification of the entire labor movement under the banner of the AFL-CIO," Kirkland said.

He said he had "strong hopes" of bringing other unions into the federation before its next convention in two years.

Kirkland said last weekend that he has talked to the United Mine Workers about affiliation. There are reports that the UMW might consider affiliation after its current round of negotiations with the coal industry. There also are reports that the mine workers might merge with the Oil, Chemical and Atomic Workers union.

Albert Shanker, president of the American Federation of Teachers, said Kirkland also has talked to the National Education Association about affiliation. Shanker said he would not oppose the affiliation of the rival union.