Prospects of a national coal mine work stoppage receded yesterday as the faction-ridden leadership of the United Mine Workers pulled together behind an effort to get wildcat strikers back to work and solve health benefit problem.

In a rare display of unity, UMW President Arnold Miller and the union's executive board made it clear they will not call a strike - or a 10 days "memorial holiday" - to protest medical benefit cutbacks.

A work stoppage was suggested earlier as a way of prodding coal operators to agree to reallocate pension and health funds, thereby permitting restoration of medical benefits cut last month because of an impending health fund deficit.

But Miller and the board meeting here for the two days in closed session, apparently decided that the money loss, which was caused in large part by continual wildcat strikes, would only be aggravated by more work stoppages.

The decision followed a vote Thursday by the executive to uphold Millers' re-election in the face of a challenge by Lee Roy Patterson, runner-up in the June 14 rank-and-file election.

Patterson said he planned to ask the Labor Department to overturn the election, but today the Miller and anti-Miller factions appeared to unite in the face of impeding conytract negotiations with coal operators this fall.

In a three-part agreement, executive board members voted to use their influence to end wildcat strikes, to continue pressure on the operators to approve a reallocation, and to authorize an independent investiagtion of possible illegal use of health benefit cards.

A member's proposal to seek the resignation of union funds' trustee Harry Huge died after Huge refused to step aside. No vote was taken.

How the board's action would affect the wildcat strikes was unclear. Some West Virginia members said they feared a nationwide wildcat strike. Associated Press reported that 30,000 Appalachian miners were out yesterday and said a non-union truck driver was shot death during an argument over a walkout near Eastern, Ky., Thursday night.