President Carter picked up the endorsement of the AFL-CIO yesterday, and promised the labor federation that he will support pro-labor legislation and work for the recognition of "the legitimate rights of labor."

In a speech to the general board of the AFL-CIO, which is made up of 104 million unions with 13.6 million members, the president also reiterated his support for Poland's workers, who won the right to form independent unions after three weeks of strikes.

"The Polish workers have demonstrated something you and I have long known -- that free trade unions are a basic instrument of democracy, and that human rights and labor rights are indistinguishable," he said.

However, while Carter was praising the "discipline," "tenacity" and "courage" of the Polish workers, the State Department continued its opposition to yesterday's decision by the AFL-CIO to establish a fund to help maintain the newly independent Polish unions.

The AFL-CIO board yesterday voted unanimously to establish the fund with an initial $25,000 contribution, and urged individual unions to contribute further.

On Wednesday, Secretary of State Edmund S. Muskie met with AFL-CIO President Lane Kirkland and, according to a State Department spokesman, cautioned him that establishment of the fund "could be misinterpreted."

The spokesman declined to elaborate, but he was clearly reflecting State Department fears that overt support for the Polish workers by American labor unions could play into the hands of the Soviet Union and might provide an excuse for the Soviets to undercut the gains won by the Polish workers.

It was also learned that late Wednesday, after his meeting with Kirkland, Muskie sent a written message to the AFL-CIO chief warning of the danger posed by establishment of the special fund.

Kirkland yesterday publicly rejected Muskie's advice, asserting that free trade unions could not be established "under a blanket of quiet diplomacy."

"The free trade union movement cannot advance on little cat feet," he said. "I will not accept the suggestion that we pussyfoot about it at all."

The AFL-CIO's endorsement of the president came as no surprise, and appeared to be generated more by fear of Republican nominee Ronald Reagan than any newly discovered enthusiasm for Carter.

Relations between the Carter administration and the labor federation have frequently been strained, and a number of union leaders have criticized the AFL-CIO board to endorse Carter yesterday, Kirkland spoke about the alternative, charging that Reagan's supporters were "among the most bitterly antilabor forces in America."

"Ronald Reagan is no friend of working people," Kirkland said."His past record proves that fact, and we must make sure that union members have the facts to match against the glib rhetoric.'"

There were no dissents from the endorsement vote, but at least two member unions of the AFL-CIO -- the Machinist and the American Federation of Government Employes -- have refused to endorse Carter. Leaders of the firefighters union said they also abstained from yesterday's AFL-CIO vote.

In his speech, the president reiterated his support for a number of organized labor's legislative objectives, and pledged to oppose any effort to weaken occupational health and safety laws.

He said his administration had witnessed the beginning of the establishment of "a partnership of government, labor and business" and that the country is involved in "nothing less than a redefinition of the way labor, business and government work together."

Carter also asserted that his economic revitalization proposals will produce "competitive industries which can meet and turn back foreign competition."