George Meany, who wrestled with many tough problems in his colorful, 24-year career as the nation's preeminent labor leader came up against the toughest of all yesterday -- saying goodbye.

The blustery labor chieftain's voice cracked, and he struggled to regain his composure as he thanked the delegates at the opening of the AFL-CIO's 13th biennial convention here "for this opportunity to serve."

Meany's brief valedictory address, delivered from a wheelchair, brought some in the audience to tears.

At one point, emotion overwhelmed the 85-year-old labor leader, and he had to start a sentence over.

". . . To God go my prayers -- prayers of thanks for granting me more than one man's share of happiness and rewards, and prayers for His continued blessing on this nation and on this labor movement and on each of you," he said.

The delegates rose in a tearful, thunderous ovation. Meany pounded his gavel to bring the convention to order. But, perhaps for the first time in his 24 years as the federation's president, he was disobeyed publicly.

The applause grew louder still and continued for 2 1/2 minutes before the delegates acceded to Meany's gavel and sat down to begin convention business.

In his last official appearance before the federation he helped create in 1955, Meany left the AFL-CIO stage the same way he entered it -- fighting for the American worker.

There were some changes, but they were mostly physical. The cigar is gone, and the ailing labor leader now must use a wheelchair.

No matter. He was always a tough talker and he talked tough yesterday. The essential Meany was there.

He said the economy is a mess because of the "ill-advised, ill-considered, ineffective and inequitable" economic policies of the Carter administration.

"Workers face tough days ahead," he said. "The national economy is a mess. America's energy problems are growing while the oil companies reap outrageous profits. Inflation is unchecked and family budgets are wrecked. The recession is at hand and in the bellwether housing industry, the depression is already here.

"Yet, the banks raise interest rates to the highest level in the nation's history."

In another thrust at the administration, Meany spoke of "national accord" the ALF-CIO signed with the administration two months ago in an attempt to give labor a bigger voice in matters affecting the nation's economy.

"It is an accord we would have willingly negotiated with the administration a year ago, but there was no real willingness on the part of the administration to treat us as a concerned partner at that time," he said. Then he indicated he was willing to let bygones be bygones.

"We have the integrity to live up to our end of the bargain. We also have the courage to blow the whistle if the administration fails to fulfill the obligations it has undertaken," he said.

With the presidential election a year away, the message was clear.

Administration officials who attended the conference -- including President Carter, who addressed it a few hours after Meany did -- got the message.

Carter had praise for the outgoing AFL-CIO chieftain saying, "No American has fought harder for economic justice for union members and for Americans who have never carried a union card.

"No American has fought harder for human dignity -- or cared more for his country."

The president acknowledged that he, as well as his predecessors, had differences with the crusty Meany.

Carter also acknowledged that his administration has made some mistakes, but said fallibility is a mark of humanity.

Carter added that some mistakes can be rectified with consistency of effort.

"Over the years, you certainly have learned the advantages of reelecting your president," he said, prompting laughter from his listeners.

Labor Secretary Ray Marshall, who followed Carter to the podium, also praised Meany. But his major purpose was to praise Carter, who Marshall said "has strongly supported . . . efforts to protect and promote the interests of the American worker. His record proves that he is responsive to the concerns of the labor movement."

Before leaving the stage, Meany urged his followers to do everything possible to keep the federation apace with changing times.

"The labor movement cannot be content with defending the status quo or reliving past glories," he said.

"The federation is the house of labor. It is well-built and ready to stand and to shelter workers long beyond the lifetime of everyone in this hall . . . It is strong and unified."