Richard Trumka, president-elect of the United Mine Workers, yesterday sought to soothe fears that he might return the troubled union to the era of disruptive wildcat strikes, and indicated a willingness to work with everybody, from the Reagan administration to the union forces who opposed his candidacy during the bitter campaign.

Trumka, elected 11 days ago, already has launched a campaign to enlist coal-state governors and members of Congress in a push for legislation that would put more miners to work and "get the nation converted from oil to coal," he said.

His ambitious agenda also includes an aggressive organizing effort in selected new coal mines in the West, to begin in January; increased grass-roots political activity by his 220,000 retired and active members, and the restoration of financial stability to the once-mighty union.

On Monday, when his transition team moves into UMW headquarters here, he will begin to go over the union books with a view toward cost-cutting and will review the people on the payroll, he said.

As for his personal agenda, Trumka plans to marry a coal miner's daughter back home in Carmichael, Pa., next Saturday. He and his wife will soon be house-hunting in the Virginia suburbs of Washington, he said.

Fielding questions in a cool, controlled manner, the 33-year-old lawyer/miner from Pennsylvania made his comments in an appearance before the Washington Press Club and in a private interview earlier.

He shrugged off lingering doubt about his eligibility to assume office next month. Although the miners' vote amounted to a landslide for Trumka, incumbent UMW President Sam Church has refused to concede the election and has revived charges that Trumka did not serve enough time in the mines to be eligible.

"Whether he ever concedes or not, on Dec. 22 we will be installed in office," Trumka said.

In a letter to the union dated Nov. 17 -- copies of which Trumka has been handing out -- Labor Department official Richard G. Hunsucker said an inquiry had upheld Trumka's elegibility.

"The election is over," said Trumka, who will become the youngest leader currently heading a major union. "As far as we're concerned, there no longer exists 'Trumka supporters' and 'Church supporters.' They're all UMW members . . . . Those doing their job are going to stay there. The people who are not doing their job will join their brothers and sisters in the coalfields."

Of the Reagan administration, he said he is "disappointed" in Reaganomics but has a "wait-and-see" attitude toward the possibility of working with the administration on programs affecting miners.

He also left open the possibility that he might take the miners back into the AFL-CIO, which includes virtually all unions except the UMW and the Teamsters. "It depends," Trumka said. "We don't know what they have to offer us right now."

The once-dominant UMW has shrunk from 400,000 members in its heyday to around 160,000 active members today (plus about 60,000 pensioners), with about 40,000 of them laid off.

The share of coal produced by UMW miners has dropped to less than half, as new mines have flowered in the West, some unorganized and some organized by another union, the Operating Engineers.

Despite economic pressures that have wrung concessions out of this and other unions, Trumka said he expects no trouble delivering on his campaign promise of "no more takeaways" for miners.

The union's founder, John L. Lewis, managed to avoid concessions during the coal industry slump of the 1950s and 1960s, he said.

Although he intends to be tough at the bargaining table, Trumka said, he hopes to avoid costly walkouts by being better prepared and by starting negotiations earlier than Church did. "You can look for a generally much more analytical . . . more aggressive approach," Trumka said.