President Carter yesterday reached out to two disparate audiences - Republican congressional leaders and the members of a friendly, pro-Carter union - in an effort to shore up support for some of his key but beleaguered legislative proposals.

Over breakfast at the White House, the president pressed 10 GOP leaders for support on the bill to implement the Panama Canal treaties and on energy, specifically the proposed "windfall profits" tax on oil industry revenues generated by his decision ordering a gradual decontrol of domestic oil prices.

House Minority Leader John J. Rhodes (R.Ariz.) said no commitments were asked for or given at the unusual meeting, which he called "useful."

Later in the day, Carter traveled to the Sheraton Park Hotel, where in a speech to a convention of the United Food and Commercial Workers international union he warned that the country is being "pulled apart by selfishness."

But, in a theme he has used increasingly in recent weeks, the president said he will not retreat from such unpopular policies as oil decontrol, even at the cost of further erosion in his already shaky political base.

"I did not campaign across this country with my family for two or three years just to sit in comfort in the White House or to read in future history books that I was once the 39th president of the United States," he said.

"I sought this office to lead - to face problems regardless of their difficulty. If the decisions I must make to safeguard the future of our country cost me some political support, then let the chips fall where they may."

The United Food and Commercial Workers union, now the single largest affiliate of the AFL-CIO, was born this week in the merger of the Retail Clerks and Amalgamated Meat Cutters unions. Its president, William W. Wynn, is a strong Carter supporter who has already endorsed the president for reelection.

This support was evident as Carter received one of the warmest receptions he has enjoyed in recent months from about 2,000 union members.

Appealing for a sense of "common purpose," Carter said that on energy and other issues where sacrifice is necessary "the greatest democratic system of government which has ever existed on earth is twisted and pulled in every direction by hundreds of well-financed, powerful and sometimes quite selfish special interest groups."

Both the speech and the meeting with Republican leaders were examples of White House efforts to rescue the administration's top-priority legislative measures, many of which are stalled in Congress.

Rep. Jack Edward (R-Ala.) said a considerable part of the discussion with Carter dealt with suggestions by several of the Republican leaders that it would be a good idea for the president to invite them down on a regular basis to talk over legislation. He did not respond directly to that proposal, Edwards said. Instead, the president said the door was always open when and if Republicans wanted to go down and talk with him. But Edwards said he got the impression Republicans would be going back for more talks.

Edwards said the Republican group didn't respond very warmly to requests for help on the Panama bill, which is due up in the House next week and on which Democrats reportedly are in deep trouble. As of now House Democrats working on the bill think the best they can hope for is passage of a chewed-up bill that the Senate might be able to repair.

But most Republicans probably would support Carter's plan for phasing out price controls on deomestic crude oil, which began June 1 and will raise domestic prices to the world level by the end of 1981. Edward said Carter could do himself a lot of good by having Republicans in periodically to talk over issues where they hand, Carter's Democratic leaders on Capitol Hill might not be too keen about his meeting privately with the opposition.