First Lady Rosalynn Carter told the Federal City Council yesterday that she is interested in making urban neighborhoods "better places to start than in Washington."

"I'm going to be spending a lot of time working in inner cities," including Washington, she told the Council's mid-winter board meeting. The council is an organization of influential business and professional people here.

Mrs. Carter attended the luncheon meeting at the Madison Hotel at the invitation of Sol M. Linowitz, president of the council and former ambassador to the Organization of American States.

Linowitz said later that Mrs. Carter had met with him earlier about cities in general and Washington specifically.

Mrs. Carter "said she had learned a great deal," Linowitz said, and was seeking ways to be helpful. He said he has suggested a list of possible areas in a 90-minute meeting recently. "I think she is less interested in the things like highways and Metro, and wants to help on the human level," Linowitz said.

Mrs. Carter told the group "in everything I've done I've seen how important the private sector is." She was influential recently in obtaining a $100,000 contribution from multimillionaire oilman Armand Hammer for an Atlanta school project.

She recently told The Washington Post that neighborhood self-help programs should rely heavily on volunteerism and private business support. She also said she is interested in a "cities in school" pilot program being organized here. Under such a program neighborhood schools would serve as centers not only for education but for a variety of community services for all ages.

Mrs. Carter's press secretary, Mary Finch Hoyt, said yesterday that Mrs. Carter has scheduled meetings with White House and executive branch agencies to "map plans for the next six months," including any progams she might have in mind for Washington.

The main speaker at the luncheon meeting in the Madison Hotel was Transportation Secretary Brock Adams, who said, "I am very much for Metro" but that the financial realities had to be faced and resolved. Adams has met with and written a number of letters ot local officials outlining future actions they must take to insure U. S. financing for Metro construction beyond 60 miles. A 100-mile system is planned and the Federal City Council recently backed completion of the full system.

"Somebody's got to keep urging (that construction) be done with a time limit and done at a certain cost," Adams said. He said that the total cost to complete 100 miles could be $8 billion. That includes $2.5 billion in interest payable over 30 years on federally guarnateed revenue bonds.

That interest was supposed to be paid by fares collected from Metro riders, but that expectation has proved optimistic.

Adams said that estimates indicate Metro will exceed available contruction funds by about $800,000. "I want to be sure that what we build fits" into the amount of money available, he said.

He also joined the Federal City Council and some locally elected officials in supporting the concept of special taxes earmarked for Metro operating deficits.