One of the broadest-based coalitions of religious, labor and civil rights groups since the civil rights days is seeking to mobilize public opinion behind the need for legislation for full employment.

"This is the priority issue for the nation," Coretta Scott King yesterday told the board of directors of the coalition, called the Full Employment Action Council. "If it (unemployment) is not solved, we will not have any hope for solving our other problems," said Mrs. King, widow of slain civil rights leader Dr. Martin Luther King, Jr. She is cochairman of the coalition.

The Council, which has been in existence for nearly four years, extended the traditional Labor day observances of last Monday into Full Employment Week, with activities scheduled for virtually every state in the union.

In preparation for the week, the National Council of Churches, the United States Catholic Conference and the National Jewish Community Relations Advisory Council churned out tens of thousands of information kits, sermon outlines, litugical aids and Labor Day proclamations. Geared to their respective constituencies, all were designed to get across the message that the national rate of unemployment is a religious as well as a political and economic issue.

In his address to the coalition's board meeting yesterday, the Most Rev. Thomas C. Kelly spelled out why. "Human lives are at stake," said the general secretary of the American Catholic hierarchy.

"Behind the statistics lie families struggling to cope with the loss of income and purpose . . . real neighborhoods and cities torn apart by the economic and social consequences of high unemployment," said Bishop Kelly.

"Our religious tradition insists that economic life exists to serve the needs of people and should reflect the broad values of social justice and human rights," he continued.

Clair Randall, general secretary of the National Council of Churches, told the board member that "Christians cannot ignore" the suffering brought about by the surrent high unemployment rate.

She warned that general affluence in this country and "the blindness to the problems of blacks and other minorities that exist in many places cause many Americans and many church members to believe that those who don't work are somehow guilty for being unemployed."

Rep. Parren J. Mitchell, (D-Md. chairman of the Congressional Black Caucus, told the coalition's board that the caucus was "available for use by you" in making contacts within the government.

He urged the approximately 50 board members present to "get on with it; go for broke now. It may be too late next year."

Mrs. King said the coalition is pressing for legislation to achieve full employment through long-range economic planning to stimulate jobs in the private sector, with a back-up system of public employment for those unable to find work elsewhere.

As a part of yesterday's board meeting, the coalition leaders met with both Senate and House of Representative leaders to discuss their concerns.

Asked to characterize the talks, Mrs. King said the congressmen "have just discovered there are some problems" in the employment situation, then added: "I think they are ready to hear more."

She said the council is also seeking a meeting with President Carter who is listed on council letterhead as a member of the board of directors.

"He signed the card" agreeing to serve on the board "while he was still governor and he never has asked us to take his name off," Mrs. King explained.