A Prince George's County judge issued a temporary injunction yesterday that will prevent 110 employes who work at the county jail from going on strike next week as their union has threatened to do.

Circuit Judge James M. Rea granted the 10-day injunction after county government attorneys argued that a strike by guards and other employes at the jail in Upper Marlboro, who are members of the American Federation of State, County and Municipal Employees would threaten the public safety.

In granting the injunction, which the union has the right to appeal, Rea ruled that a strike would reduce the manpower of the county's Department of Corrections "to the point that it will be unable to care for prisoners adequately or protect the security of the residents of Prince George's County."

The injunction does not apply to the other 7,400 members of the public employes' union, such as building inspectors, landfill operators and clerical workers. They are planning to walk off the job next Tuesday if no settlement in their longstanding contract dispute with the county is reached.

The union and the county have been negotiating for more than a year. Since July, members of the union have been working without the cost-of-living increases granted all other county employes.

About three weeks ago a tentative agreement was reached that granted the union members a 4.7 percent wage increase. Although the union membership ratified that agreement, County Executive Lawremce J. Hogan vetoed it, apparently believing it would appear that he had capitulated to pressure by the union and some of his political rivals on the County Council.

With yesterday's injunction, the county began a series of legal maneuvers to delay or minimize the effects of a strike.

Union officials said yesterday they will contest the injunction.

Hogan said yesterday: "This decision supports the county's claims that a walkout by prison guards would endanger public safety. I pledge . . . to protect the safety of our citizens."

In a related development yesterday, an independent mediation board denied the county's request to change a previous ruling that an impasse in the contract dispute had been reached.

That earlier ruling set into motion the union's strike countdown, which permits a legal strike next Tuesday. Hogan had tried to stop the countdown and declare the strike illegal.