The Carter administration served notice yesterday that it will rely on local and state authorities to keep peace in the coalfields for the present rather than call up federal forces to protect miners and the mines.

The Defense and Justice departments said last night they were taking no action at this time to increase the level of federal involvement in the 91-day-coal strike.

"Our attitude has been, and still is, to look for a peaceful settlement and to avoid saber rattling." said Mark Sheehan, assistant director of public information at the Justice Department.

The law gives the president authorities to use federal troops to enforce court orders - such as a back-to-work order to miners - but a U.S. Army spokesman said no units have been alerted.

President Carter sent telegrams yesterday to governors of all the coal-producing states advising them of their "primary responsibility" for preventing violence.

"I have instructed the attorney general to work closely with you to make sure the law is obeyed, that violence is avoided, and that the health, safety and welfare of all citizens is projected. As in the past the primary responsibility for this protection rests with you. My action in no way changes that or increases the level of federal particiaption in this area," the president told the governors.

Nevertheless, the stage was set for a potential test of strength between union and government in the coalfields.

The United Mine Workers members already have domonstrated their power. The threat of union retalliation or violence caused many non-union mines to close along with union ones.This is the labor power that Carter confronts now in his biggest domestic crisis.

In eastern coal states, non-union coal companies that closed during the strike might be more ready to reopen under the protection of a federal order. However, this is difficult to predict because factors such as the family ties owners of thse non-union mines have also weighted in some of the closings.

At the state level, governors yesterday adopted a cautious posture in regard to plans for protecting the coal companies, miners who obey a back-to-work command, and trucks and railroads hauling the coal.

State government spokesmen said they believed that state police, and if necessary National Guardsmen could adequately protect coal company property and miners going to and from work. Beyong that, theysaid, protecting coal shipments was more difficult task.

Indiana activated about 300 National Guardsmen three weeks ago to help protect trucks carrying coal. But no other Guard units had been activated or alerted as of last night, and a spokesman said the Indiana action was "winding down".

The emphasis at the state level appeared to be on not inflaming a tense situation with undue threats or shows of muscle.

In Kentucky, where violence has flared repeatedly since the strike began, Gov. Julian Carroll said yesterday that he did not intend to take emergency action "until there is a demonstration need for it." A spokesman said Carroll did not want to "second guess" the reaction to an invocation of Taft-Hartley provisions.

However, many of Kentucky's 5,500 Army Guardsmen called their headquarters yesterday wanting to know if they were about to be called up. A spokesman said that if any units were called, these would include the military police unit in Louisville.

Miners themselves make up a significant percentage of National Guard units in such states as Kentucky, West Virginia and Pennsylvania. Several of Pennsylvania's National Guard military police units are drawn from western mining counties.

Gov. Milton J. Sharpp of Pennsylvania plans to meet with state law enforcement and military officials later this week to plan a strategy for keeping the peace.

Short of sending in federal troops the U.S. government's power to intervene to enforce the law is limited officials said. The president has the authorithy to federalize National Guard units - a measure that would at least save money for hard-pressed state budgets.

Also, the Justice Department can prosecute persons assaulting federal mine safety inspectors, interfering with coal shipped in interstate commerce, or illegally possessing explosives. But a Justice Department official said: "The federal road on enforcement is relatively narrow."