President Carter promised representatives of a coalition of labor, civil rights and other organizations yesterday that he would give careful thought to their request for an increase in the administration's recommended $2.50-an hour minimum wage level.

But according to Clarence Mitchell, chief lobbyist for the NAACP, the President made no commitments during the meeting with the Coalition for a Fair Minimum Wage.

Mitchell, AFL-CIO President George Meany, Dorothy Height of the National Council of Negro Women and Msgr. Francis Lally of the U.S. Catholic Conference met Carter for about 20 minutes yesterday.

A White House official said specific minimum wage figures were not discussed during the meeting. The AFL-CIO is seeking an increase in the minimum wage, now $2.30 an hour, to $3 an hour.

Mitchell said the group presented Carter with statistics showing the administration proposal would leave some 3 million working poor below the poverty level in 1980.

"This is an affort on the part of American citizens to see our people reach a level where they can live in dignity," he said. "It did seem to me that the President warmed up to that thought."

In other developments yesterday, the White House announced that Saudi Arabia's Crown Prince Fahd will meet Carter at the White House May 24 and 25. The Meeting is part of an initial round of talks with major leaders in the Middle East in an attempt to find a Middle East peace settlement.

The White House also announced Carter will nominate Eleanor Holmes Norton, 39, chairman of the New York City Commission on Human Rights, as chairman of the Equal Employment Opportunity Commission, and Marion Edey, 32, chairman of the League of Conservative Voters, to be a member of the Council on Environmental Quality.